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1
vote
0answers
58 views

Homology and Exterior Square

Let $G$ be a finite group and $G \wedge G$ denote the exterior square of $G$. It is well known that the second integral homology $H_2(G,\mathbb{Z})$ is the kernel of homomorphism $x \wedge y \mapsto ...
10
votes
2answers
456 views

How hard (P, NP, NP-hard) is it to compute Schur norms of matrices (as multipliers)?

Given a matrix $A\in M_n(\mathbb{C})$, I will denote by $||A||_\infty$ the operator norm of $A$, as seen acting on the Hilbert space $\mathbb{C}^n$. This makes $M_n(\mathbb{C})$ into a Banach space ...
0
votes
0answers
113 views

A question about multiplier algebra of $C_0(G)\otimes C_b(G)$ for a locally compact group $G$

Let $G$ be locally compact group. How we can show that $$ M(C_0(G)\otimes C_b(G))=C_b(G,C_b(G)). $$ ($M(C_0(G)\otimes C_b(G))$ is the multiplier algebra of $C_0(G)\otimes C_b(G)$)
25
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2answers
1k views

Why are Schur multipliers of finite simple groups so small?

Given a finite simple group $G$, we can consider the quasisimple extensions $\tilde G$ of $G$, that is to say central extensions which remain perfect. Some basic group cohomology (based on the ...
10
votes
1answer
370 views

Schur multipliers over non-algebraically closed ground fields?

Recently some arithmetic dynamicists came to town, bringing with them some interesting problems in arithmetic geometry. I started thinking a bit about one of their problems, and it got me wondering ...