bio | website | www10.mathematik.uni-wuerzbur… |
---|---|---|
location | Würzburg, Germany | |
age | ||
visits | member for | 4 years, 6 months |
seen | 2 days ago | |
stats | profile views | 3,760 |
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. |