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Wild problems in the theory of representations of \(*\)-algebras given by generators and relations. (English. Russian original) Zbl 0939.16010

Ukr. Math. J. 47, No. 1, 81-90 (1995); translation from Ukr. Mat. Zh. 47, No. 1, 70-78 (1995).
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.
Reviewer: G.F.Us (Kyïv)

MSC:

16G60 Representation type (finite, tame, wild, etc.) of associative algebras
46K10 Representations of topological algebras with involution
46L35 Classifications of \(C^*\)-algebras
16R50 Other kinds of identities (generalized polynomial, rational, involution)
16W10 Rings with involution; Lie, Jordan and other nonassociative structures
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