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- W3037057838 abstract "Let $k$ be a field, $G$ be an abelian group and $rin mathbb N$. Let $L$ be an infinite dimensional $k$-vector space. For any $min End_k(L)$ we denote by $r(m)in [0,infty ]$ the rank of $m$. We define by $R(G,r,k)in [0,infty]$ the minimal $R$ such that for any map $A:G to End_k(L)$ with $r(A(g'+g'')-A(g')-A(g''))leq r$, $g',g''in G$ there exists a homomorphism $chi :Gto End_k(L)$ such that $r(A(g)-chi (g))leq R(G, r, k)$ for all $gin G$. We show the finiteness of $R(G,r,k)$ for the case when $k$ is a finite field, $G=V$ is a $k$-vector space $V$ of countable dimension. We actually prove a generalization of this result. In addition we introduce a notion of {it Approximate Cohomology} groups $H^k_{mathcal F} (V,M)$ (which is a purely algebraic analogue of the notion of $epsilon$-representation (cite{ep})) and interperate our result as a computation of the group $H^1_{mathcal F} (V,M)$ for some $V$-modules $M$." @default.
- W3037057838 created "2020-07-02" @default.
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- W3037057838 creator A5091670796 @default.
- W3037057838 date "2017-02-04" @default.
- W3037057838 modified "2023-09-27" @default.
- W3037057838 title "Appoximate Cohomology" @default.
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