most recent 30 from http://mathoverflow.net 2013-05-24T02:12:15Z http://mathoverflow.net/feeds/user/16682 http://www.creativecommons.org/licenses/by-nc/2.5/rdf http://mathoverflow.net/questions/130376/resolutions-of-lie-algebras jim stasheff 2013-05-11T23:18:57Z 2013-05-12T04:26:09Z

<p>We have a good notion of dgc algebra resolutions of commutative algebras. Is there an explicit construction of a dg Lie algebra resolution of a Lie algebra?</p>

http://mathoverflow.net/questions/130337/coordinate-free-koszul-tate jim stasheff 2013-05-11T13:58:57Z 2013-05-11T15:11:06Z

<p>Tate's original construction involved choosing cocycles representing the cohomology to be killed. here is it written a coordinate free treatment, perhaps via a slitting of the module of indecomposables?</p>

http://mathoverflow.net/questions/130191/higher-order-noether-identities jim stasheff 2013-05-09T18:25:07Z 2013-05-09T21:01:04Z

<p>Noether's 2nd variational theorem gives a correspondence between symmetries of a Lagrangian and Noether identities = relations among the E-L equations.</p> <p>How about relations among relations among the E-L equations cf. syzygies?</p>

http://mathoverflow.net/questions/129991/brst-cohomology-defintion jim stasheff 2013-05-07T17:39:34Z 2013-05-08T16:20:26Z

<p>Is there written any where a full definition of BRST cohomology? all I;ve found so far is BRST cohomology in <strong><em>_</em></strong>. As far as I can see, BRST cohomology is the cohomology of a complex in which the differential has at least a piece that `looks like' the Chevalley Eilenberg differential</p> <p>that seem s to include all known examples but is hardly a precise definition</p>

http://mathoverflow.net/questions/128968/coordinate-free-euler-lagrange jim stasheff 2013-04-28T00:11:52Z 2013-04-28T00:11:52Z

<p>The variational approach is to seek critical points in terms the Euler-Lagrange variational derivatives $E_a(S_0)$ of a local function $S_0.$ The zero locus does not depend on coordinates. Where is there a similalry coordinate free description of the corresponding Jacobian ideal?</p>

http://mathoverflow.net/questions/128415/general-jacobian-ring jim stasheff 2013-04-22T23:36:56Z 2013-04-22T23:36:56Z

<p>What is the maximal situation in which one speaks of the Jacobian ring or Jacobian ideal? Can one go beyond smooth functions?</p>

http://mathoverflow.net/questions/127631/felder-kazhdan-classical-me jim stasheff 2013-04-15T15:02:30Z 2013-04-15T15:02:30Z

<p>Has there been any follow up by anyone to Giovanni Felder, David Kazhdan, The classical master equation (arXiv:1212.1631)? Other than on nlab, I haven't found any citations.</p>

http://mathoverflow.net/questions/126705/sh-lie-algebra-cohomology jim stasheff 2013-04-06T13:13:56Z 2013-04-07T10:14:24Z

<p>For sh Lie algebra cohomology, is there written anywhere a description of H^1(L;L) as sh derivations mod inner ones?</p>

http://mathoverflow.net/questions/126305/bar-cobar-or-cobar-bar jim stasheff 2013-04-02T19:42:40Z 2013-04-02T19:53:16Z

<p>What is the standard or best reference for the adjointnes of bar and cobar constructions?</p>

http://mathoverflow.net/questions/123417/bar-construction-for-algebras-with-unusual-grading-of-d jim stasheff 2013-03-02T15:22:41Z 2013-03-02T15:35:01Z

<p>The bar construction is usually applied to differential graded algebras with differential $d$ of degree +1 or -1. Using multiple (de)suspensions, it also works for $d$ of any degree $\neq 0$. Is this fact mentioned in the literature, or is it folklore? -- Jim Stasheff </p>

http://mathoverflow.net/questions/123413/simplicial-path-and-loop-spaces/123418#123418 jim stasheff 2013-03-02T15:27:45Z 2013-03-02T15:27:45Z

<p>Have you considered the sequence Omega X --> PX --> X in the two categories where Omega denotes based loop space and P based path space</p>

http://mathoverflow.net/questions/122420/koszul-alg-deformations jim stasheff 2013-02-20T16:52:38Z 2013-02-20T16:52:38Z

<p>Is it known the maximal class of Koszul algebras for which any deformation is Koszul?</p>

http://mathoverflow.net/questions/115911/rational-homotopy-of-a-manifold jim stasheff 2012-12-09T19:23:43Z 2013-02-09T12:55:29Z

<p>Given a finite dim rational homotopy type satisfying Poincaré duality, what is the best reference to when it is the rational homotopy type of a fin dim manifold?</p>

http://mathoverflow.net/questions/110578/tensor-products-not-iterated jim stasheff 2012-10-24T19:55:28Z 2012-10-25T00:51:16Z

<p>3-fold tensor products are usually presented in terms of the natural isomorphism of iterated tensor porducts. Where is there a treatment of 3-fold tensor products without reference to 2-fold?</p>

http://mathoverflow.net/questions/109001/exact-dg-poisson-algebra jim stasheff 2012-10-06T14:20:10Z 2012-10-08T17:32:24Z

<p>A symplectic manifold gives rise to a Poisson algebra. If the symplectic form is exact, how is this revealed in the algebra?</p>

http://mathoverflow.net/questions/106741/deformation-of-noethers-1st-theorem jim stasheff 2012-09-09T17:18:33Z 2012-09-09T17:18:33Z

<p>Has anything been written on the following: Noether's 1st variational theorem establishes a correspondence betwween symmetries and invariants. If we deform the symmetries, the invariants deform as... How about if the Lie algebra of symms is deformed as an L-infty-algebra?</p>

http://mathoverflow.net/questions/99735/unfolding-as-resolution jim stasheff 2012-06-15T18:56:15Z 2012-08-24T17:02:59Z

<p>Has anyone described `unfolding' as used in mathphysics (e.g. on-shell AND off-shell) as analogous to a resolution in algebra - higher derivatives are unfolded in terms of new variables?</p>

http://mathoverflow.net/questions/103778/lie-algebra-coboundary jim stasheff 2012-08-02T12:46:40Z 2012-08-11T13:27:44Z

<p>There seems to be a problem in the literature about the definition of the 'standard' coboundary on the 'Cartan-Chevalley-Eilenberg' algebra - the problem is the signs!</p> <p>Where/when did things go wrong? And what's the best way to reference so the next generation learns only the correct signs?</p> <p>with more precision: the usual C-E coboundary has two summations - for the module structure and for the algebra each is separately correct in all references but some have the sum squaring to zero and others not -i.e. wrong relative sign for the two summations</p> <p>Here's the original reference: Chevalley, Claude; Eilenberg, Samuel (1948), "Cohomology Theory of Lie Groups and Lie Algebras", Transactions of the American Mathematical Society (Providence, R.I.: American Mathematical Society) 63 (1): 85–124, </p> <p>and some others that may or may not copy the first Hilton, P. J.; Stammbach, U. (1997), A course in homological algebra, Graduate Texts in Mathematics, 4 (2nd ed.), Berlin, New York: Springer-Verlag, ISBN 978-0-387-94823-2, MR 1438546 Knapp, Anthony W. (1988), Lie groups, Lie algebras, and cohomology, Mathematical Notes, 34, Princeton University Press, ISBN 978-0-691-08498-5, MR 938524</p> <p>The signs are correct (I believe) in</p> <p><a href="http://www.scholarpedia.org/article/User:Jan_A._Sanders/An_introduction_to_Lie_algebra_cohomology/Lecture_1#the_coboundary_operator" rel="nofollow">http://www.scholarpedia.org/article/User:Jan_A._Sanders/An_introduction_to_Lie_algebra_cohomology/Lecture_1#the_coboundary_operator</a></p>

http://mathoverflow.net/questions/104467/a-homotopy-equivalence-between-total-spaces-in-a-hurewicz-fibration-which-is-no/104477#104477 jim stasheff 2012-08-11T13:07:37Z 2012-08-11T13:07:37Z

<p>I think James-Whitehead are quite relevant:</p> <p>MR0068836 Reviewed James, I. M.; Whitehead, J. H. C. The homotopy theory of sphere bundles over spheres. II. Proc. London Math. Soc. (3) 5, (1955). 148–166. </p> <p>MR0061838 Reviewed James, I. M.; Whitehead, J. H. C. The homotopy theory of sphere bundles over spheres. I. Proc. London Math. Soc. (3) 4, (1954). 196–218. </p>

http://mathoverflow.net/questions/104447/minimal-koszul-tate-resolutions jim stasheff 2012-08-10T23:40:01Z 2012-08-10T23:40:01Z

<p>In what generality of commutative associative algebras does there exist a <em>minimal</em> Koszul-Tate resolution? or what is the most general condition known?</p>

http://mathoverflow.net/questions/96340/symplectic-boundary jim stasheff 2012-05-08T14:15:26Z 2012-08-02T16:33:14Z

<p>Is there any work on manifolds (perhaps contact) with symplectic boundary (not asking about the boundary of a symplectic manifold)?</p>

http://mathoverflow.net/questions/90045/schur-multipliers-for-lie-algebras jim stasheff 2012-03-02T15:23:19Z 2012-06-23T14:19:38Z

<p>Schur multipliers for group extensions and for Lie groups also Where are they written for Lie algebras?</p>

http://mathoverflow.net/questions/99734/superdiff-forms-and-tensors jim stasheff 2012-06-15T18:52:40Z 2012-06-15T18:52:40Z

<p>Where is it written that symmetric tensors (i.e. with multiindices) occur as the coefficient functions of super differential forms or rather odd differential forms?</p>

http://mathoverflow.net/questions/97703/list-of-hall-basis jim stasheff 2012-05-22T22:00:37Z 2012-05-23T14:36:51Z

<p>Anyone know a place where the standard Hall basis is listed up to at lest 5 fold brackets? and for gradedLie algebras?</p> <p>The rules are clear but I'd rather not turn the crank myself. Google search did not get me there quickly.</p>

http://mathoverflow.net/questions/93438/euler-class-in-the-non-compact-case jim stasheff 2012-04-07T18:20:34Z 2012-04-16T12:36:27Z

<p>Does anyone have a reference for:</p> <p>The Euler-class for an open non-compact manifold possibly with twisted coefficients (if the group action on the manifold does not preserve orientation) and/or for a compactification e.g. the one point compactification</p> <p>jim </p>

http://mathoverflow.net/questions/89644/how-to-find-colin-days-phd-thesis/89665#89665 jim stasheff 2012-02-27T13:58:39Z 2012-04-05T08:38:03Z

<p>I appreciate the interest shown. It apparently is on microfiche. I am in contact with the UNC math library and hope to have access I can share.</p> <p><b>Update</b>: It is now available at</p> <p><a href="http://hans.math.upenn.edu/~jds/" rel="nofollow">http://hans.math.upenn.edu/~jds/</a></p> <p>scroll down to Colin...</p> <p>Please let me know if you access it or if you have trouble accessing it.</p>

http://mathoverflow.net/questions/12144/classifying-space-of-a-group-extension/90708#90708 jim stasheff 2012-03-09T15:25:27Z 2012-03-09T15:25:27Z

<p>@There is an equivalence between grouplike homotopy commutative spaces and double loop spaces</p> <p>No, grouplike homotopy commutative is not enough. Double loop spaces have much more in thee way of higher homotopies, even if the space were to have a strictly associative homotopy commutative structure. That was one of the motivations for operads. Also see JF Adams: 10 types of H-spaces.</p>

http://mathoverflow.net/questions/90582/b-gamma-constructed jim stasheff 2012-03-08T14:56:39Z 2012-03-08T15:46:50Z

<p>In his pioneering paper on foliations, Haefliger obtains $B\Gamma_q$ as the representing space of a functor, NOT by construction analogous to the bar construction. Who made that connection first? Bott?</p>

http://mathoverflow.net/questions/90400/the-set-of-all-principal-g-bundles-over-all-spaces jim stasheff 2012-03-06T22:07:34Z 2012-03-07T04:31:14Z

<p>What is a good notation for the 'set' (or stack if you insist) of all principal G bundles over 'all' spaces for given G? BG is way over used. How about Bun(G)?</p>

http://mathoverflow.net/questions/90116/functor-before-cat jim stasheff 2012-03-03T14:03:42Z 2012-03-03T14:33:03Z

<p>As i read the literature, derived functors were there several years before derive categories - right?</p>

http://mathoverflow.net/questions/123417/bar-construction-for-algebras-with-unusual-grading-of-d jim stasheff 2013-03-02T15:23:52Z 2013-03-02T15:23:52Z

I meant to ask for a reference Don't know why I'm listed as unknown?? jim stasheff

http://mathoverflow.net/questions/110578/tensor-products-not-iterated jim stasheff 2012-10-25T13:47:49Z 2012-10-25T13:47:49Z

Thanks, Todd - Matho didn't alert me to these answers. And YES Jim is the proper form of address. The question was deliberately ambiguous. I will look into the unbiased monoidal description. A colleague had a particular case in mind; I will look it up and describe more precisely. Meanwhile, how about this: Suppose I have rings R and S AND MODULES A, B and C such that A\otime_R B and B \otimes _S are defined, when does it make sense to talk about a triple tensor product over what?

http://mathoverflow.net/questions/103778/lie-algebra-coboundary jim stasheff 2012-09-09T17:14:41Z 2012-09-09T17:14:41Z

Vlad, you say `all signs are recovered in a jiffy via the interpretation of (co)homology as Tor/Ext. ' That sounds clever except I don't undertstand that at all. Do you mean that only a correct choice of signs will give cohomology? i.e. d^2 =0?

http://mathoverflow.net/questions/97703/list-of-hall-basis/97725#97725 jim stasheff 2012-05-24T13:56:57Z 2012-05-24T13:56:57Z

I had no idea that Omar's suggestion would do the computation and display the results rather than being software I could download and compute. A marvelous resource! I googled a bit more until I found CoRoPa, which does compute it.) – Omar Antol&#237;n-Camarena 22 hours ago I'd tried gogling but got nowhere near!

http://mathoverflow.net/questions/97703/list-of-hall-basis/97725#97725 jim stasheff 2012-05-24T13:25:44Z 2012-05-24T13:25:44Z

Many thanks for information and enlightenment. Will have a look to see if I can find a list up through 5-fold brackets. Even with SAGE, tables are still useful.

http://mathoverflow.net/questions/19989/how-can-i-tell-whether-a-poisson-structure-is-symplectic-algebraically/20023#20023 jim stasheff 2012-05-02T14:53:57Z 2012-05-02T14:53:57Z

If the Poisson algebra is an algebra of smooth functions and satisfies your symplectic criteria, how does one construct the corresponding form?

http://mathoverflow.net/questions/89644/how-to-find-colin-days-phd-thesis/89665#89665 jim stasheff 2012-04-07T18:19:02Z 2012-04-07T18:19:02Z

Daniel, Thanks for doing that.

http://mathoverflow.net/questions/90400/the-set-of-all-principal-g-bundles-over-all-spaces/90426#90426 jim stasheff 2012-03-08T14:02:08Z 2012-03-08T14:02:08Z

That does clarify the relation, but notice how many words it required.

http://mathoverflow.net/questions/90400/the-set-of-all-principal-g-bundles-over-all-spaces/90418#90418 jim stasheff 2012-03-07T13:15:31Z 2012-03-07T13:15:31Z

I can live with Spaces/BG since it is not previously used and will encourage the reader to understand what it denotes.

http://mathoverflow.net/questions/90400/the-set-of-all-principal-g-bundles-over-all-spaces/90426#90426 jim stasheff 2012-03-07T13:12:02Z 2012-03-07T13:12:02Z

Perhaps no confusion <i>within</i> alg-geom, but we are not all alg-geometers. So your BG is a category and alg-geom has no use for a classifying space for G-bundles? or it has some other symbol?

http://mathoverflow.net/questions/90045/schur-multipliers-for-lie-algebras/90344#90344 jim stasheff 2012-03-07T12:58:49Z 2012-03-07T12:58:49Z

What is the meaning of nonabelian in that reference? I skimmed the paper and am missing any mention of the function in relation to extensions.

http://mathoverflow.net/questions/86082/homotopy-fibre-sequence-of-classifying-spaces jim stasheff 2012-03-06T22:13:07Z 2012-03-06T22:13:07Z

That requires knowing how the transgression BH --&gt; B G/H behaves. In many cases, the Eilenberg_Moore spectral seq is more efficient. For lots of examples, consult Borel or Greub-Hlapernin-VanStone vol III

http://mathoverflow.net/questions/90116/functor-before-cat jim stasheff 2012-03-03T16:18:08Z 2012-03-03T16:18:08Z

I think is this provides some background between the homological/homotopical algebra and the derived cat communities. Some of us didn't pick up on the derived cat language, but charged ahead using resolutions and the yoga that one resolution was as good as another - e.g the bar resolution and relatives.

http://mathoverflow.net/questions/90045/schur-multipliers-for-lie-algebras/90054#90054 jim stasheff 2012-03-03T14:17:13Z 2012-03-03T14:17:13Z

That's it, though she calls them `factor functions', which google can't find (easily). Care to identify yourself? How came you to be aware of her thesis? Tom Lada was on her committee - I should have asked him.

http://mathoverflow.net/questions/71070/higher-order-structure-by-higher-order-derivatives/71119#71119 jim stasheff 2011-07-25T11:48:10Z 2011-07-25T11:48:10Z

Jos\'e, That is the one I was after. Apologies for the vagueness of my question,thinking it did have something to do with Frobenius manifolds, but having not found the answer in Dubrovin, I thought that too might be a faulty memory.