3,706 reputation
11337
bio website www10.mathematik.uni-wuerzbur…
location Würzburg, Germany
age
visits member for 4 years, 6 months
seen 2 days ago

Interests: Mathematical Physics, Deformation Quantization, Poisson and Symplectic Geometry, Noncommutative Geometry. Fréchet algebraic deformations.


Jul
30
reviewed Close Angle sum of triangle in Schwarzschild solution
Jul
30
reviewed Close Why only Normed Linear Spaces?
Jul
29
reviewed Close Which branch should I choose for my master degree? PDE or Dynamical Systems
Jul
27
comment Check symplectomorphism property on infinitesimal generators
For a connected LIe group, this is really a standard argument in Lie theory since any neighbourhood of the identity generates the connected component of the identity. In the nonconnected case you can not say anything reasonable: think of a discrete Lie group with non-symplectic group action...
Jul
23
reviewed Close Determinants of tensors
Jul
21
reviewed Close Understanding the asserted variation in a WASEP particle model
Jul
14
comment When to postpone a proof?
sad but true...
Jul
14
comment Stinespring's dilation without $C^{\ast}$-algebras
... among them the star product algebras which are not even algebras over $\mathbb{C}$ but over the formal power series ring $\mathbb{C}[[\hbar]]$. This exmplains why we were interested to extend the notions to more general scalars. Thanks also for the $\ell^1$ example. This I didn't know. I always use the continuous functions on the sphere with -involution given by complex conjugation *and the antipodal map, as you indicated also in your above comment. This has really creepy features for many reasons :)
Jul
14
comment Stinespring's dilation without $C^{\ast}$-algebras
@YemonChoi. Thanks for your comments. And yes: H and K are sort of important. They are the abstracted version of what one needs in view of $C^*$-algebras. We (i.e. Henrique Bursztyn and I) used that a lot when discussing all sorts of Morita theory for -algebras. The upshot is somehow that the (strong) Morita theory of C-algebras is indeed algebraic, but the Picard group is not: there are subtle differences even for C*-alegbras. To get a reasonable theory for *-algebras, H and K are sort of essential (for technical reasons) The main point is that there are many examples beyond $C^*$...
Jul
14
revised Stinespring's dilation without $C^{\ast}$-algebras
oops, most important thing forgotten ;)
Jul
14
comment Stinespring's dilation without $C^{\ast}$-algebras
@Nik Weaver: (complete) positivity is in fact an algebraic notion. For *-algebras over $\mathbb{C}$ this has been investigated a lot by Schmuedgen in his unbounded operator algebra book, for more general *-algebras, please take a look at my answer.
Jul
14
reviewed Leave Open Stinespring's dilation without $C^{\ast}$-algebras
Jul
14
answered Stinespring's dilation without $C^{\ast}$-algebras
Jul
10
reviewed Leave Open the true reason of the incompleteness of formal systems
Jul
6
reviewed Leave Open Titles composed entirely of math symbols
Jun
29
revised Good books on Geometric Theory of Dynamical Systems
oops, typo
Jun
29
answered Good books on Geometric Theory of Dynamical Systems
Jun
29
comment Automorphism group of a fiber bundle surjects onto diffeomorphism group?
@Robert Bryant: That's cute, thanks a lot. Should have thought more about the problem myself :)
Jun
28
comment Automorphism group of a fiber bundle surjects onto diffeomorphism group?
@Igor Belegradek: thanks for the example!
Jun
28
comment Automorphism group of a fiber bundle surjects onto diffeomorphism group?
@Igor Belegradek: well, I have nothing special in mind. The question came up once in a lecture of mine. I would be happy to see a counter-example etc just to get an impression what one should expect here.