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Identities of algebras and their representations. Transl. from the Russian by A. M. Shtern. Transl. ed. by Simeon Ivanov. (English) Zbl 0827.17001

Translations of Mathematical Monographs. 138. Providence, RI: American Mathematical Society (AMS). xiii, 318 p. (1994).
This monograph is a translation from the Russian edition (1989) (for the review see Zbl 0673.17001). It concerns the latest achievements in the area of polynomial identities in Lie algebras, and their representations. The author of the book is one of the leading specialists in the theory of polynomial identities. He introduced and developed the technique of 2- words and \(\alpha\)-functions that enabled him (and many others) to solve a large number of classical problems in ring theory.
This English translation of the monograph provides an excellent opportunity for specialists in ring theory to become familiar with these significant advances in the theory of algebras satisfying polynomial identities.

MSC:

17-02 Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras
17B01 Identities, free Lie (super)algebras
16R10 \(T\)-ideals, identities, varieties of associative rings and algebras
17B99 Lie algebras and Lie superalgebras
17B30 Solvable, nilpotent (super)algebras

Citations:

Zbl 0673.17001