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 …

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 …

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 …

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 …

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 …

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) …

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 …

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 …

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 …