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Zbl 0939.16010
Piryatinskaya, A.Yu.; Samoilenko, Yu.S.
Wild problems in the theory of representations of $*$-algebras given by generators and relations. (English. Russian original)
[J] Ukr. Math. J. 47, No.1, 81-90 (1995); translation from Ukr. Mat. Zh. 47, No.1, 70-78 (1995). ISSN 0041-6053

The authors consider the representations of the $*$-algebra with the generators $a_k,a_k^*$, $k=1,\ldots,n$ which satisfy the polynomial relations $P_j(a_1,\ldots,a_n,a_1^*,\dots,a_n^*)=0$, $j=1,\dots,m$. Connections between the factor-wild $*$-algebras (NGCR, in other terms) and the pair-wild $*$-algebras are investigated. It is shown that a pair-wild $*$-algebra is a factor-wild $*$-algebra, but the converse of this statement is not true.
[G.F.Us (Ky\" iv)]

MSC 2000:: *16G60 Representation type of noncommutative rings and modules
46K10 Representations of rings with involution
46L35 Classifications and factors of C*-algebras
16R50 Other kinds of identities of assoc. rings
16W10 Associative rings with involution

Keywords: $*$-algebras; factor-wild algebras; categories of $*$-algebra representations; pair-wild algebras

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