0
votes
1answer
104 views
Isomorphic maximal commutative semi-simple sub algebras of M_n(C).
When giving A_1,A_2 two Isomorphic maximal commutative semi-simple sub algebras of M_n(C).
Are these algebras conjugate in M_n(C). Namely, is there exists a regular matrix P such t …
1
vote
0answers
149 views
Algebra out of a set of modules of a Lie algebra? Fusion
The problem I faced is how to organize a set of finite-dimensional irreducible representations $U_\alpha$ of some simple Lie algebra $g$ into an associative algebra $A$ that contai …
3
votes
2answers
306 views
surjectivity of irreducible representation
I don't know how to show the following:
Let $A$ be an associative algebra (not necessary finite-dimensional) and $p\colon A\to End(V)$ be it irreducible finite-dimensional represe …
1
vote
0answers
98 views
Preservation of direct sums and finite generation
I asked this question on Mathematics - Stack Exchange (MSE). Having figured out out how to handle the problem in an extremely particular case, I also posted it as an answer (in the …
12
votes
1answer
463 views
Does $\mathbb{K}[G]\simeq\mathbb{K}[H]$ for some field $\mathbb{K}$ of characteristic $p$, imply $\mathbb{F}_p[G]\simeq\mathbb{F}_p[H]$?
Due to the first (and very helpful) answer I received, I've reformulated the question a little: $G$ and $H$ are now assumed to be $p$-groups.
Let ${p}$ be a prime, and let $\mathb …
3
votes
1answer
551 views
$A_{\infty}$ structure of (co)homology of a space
Let $X$ be a topological space, and $Homeo(X)$ the group of self-homeomorphisms of $X$.
(1) What is the exact meaning of: $H^*(X)$ is a an $A_\infty$-module over $Homeo(X)$?
(2) …
0
votes
1answer
245 views
Algebras with a degenerate trace form
Let the bilinear trace form of a finite-dimensional associative algebra be defined as:
$(u,v) \mapsto Tr(L_u L_v)$
For $L_u$ the linear map given by multiplication on the left by …
6
votes
2answers
802 views
What’s the sense in which A_\infty algebras are “deformable”?
I realise this is a very vague question! I've heard people say that A∞ algebras are the right homotopy-theoretic generalization of usual associative algebras, because you can …
1
vote
1answer
427 views
Is the multiplication beetween even numbers an associative algebra?
We were discussing about the possibility of having an algebra over a field which is associative but has not the unity. Does it exist?
It has been proposed as a counterexample the …

