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Combinatorial aspects of Capelli identities and structure of algebras. (English) Zbl 0985.16016
Krob, Daniel (ed.) et al., Formal power series and algebraic combinatorics. Proceedings of the 12th international conference, FPSAC’00, Moscow, Russia, June 26-30, 2000. Berlin: Springer. 785-788 (2000).
Summary: The combinatorial properties of the system of Capelli identities are investigated. These properties have enabled the author to develop a characteristic-free approach to the structure theory of algebras satisfying Capelli identities with an arbitrary set of multilinear operations. The structure theory of those algebras is analogous to that of PI-algebras and finite-dimensional algebras. The obtained combinatorial properties also clarify the proof of the Braun-Kemer-Razmyslov theorem on the radical problem of an associative PI-algebra.
For the entire collection see [Zbl 0941.00013].
16R10 \(T\)-ideals, identities, varieties of associative rings and algebras
16R50 Other kinds of identities (generalized polynomial, rational, involution)