Koshlukov, Plamen Algebras with polynomial identities. (English) Zbl 0976.16019 Mat. Contemp. 16, 137-186 (1999). This survey is based on the notes for a minicourse delivered by the author at the 15th Escola de Álgebra held at Canela. It gives an introduction to selected combinatorial methods and results of PI theory. The topics touched include the Amitsur-Levitzki theorem, the Nagata-Higman-Dubnov-Ivanov theorem, Regev’s tensor product theorem, the Shirshov theorem, the Kurosh problem, applications of the representation theory of symmetric and general linear groups to the study of identities, the Specht problem, the T-ideal of identities of \(2\times 2\) matrices, identities and weak identities of Lie and Jordan algebras, identities in positive characteristic. Proofs are often substituted by hints or references. Reviewer: M.Domokos (Budapest) Cited in 1 Document MSC: 16R10 \(T\)-ideals, identities, varieties of associative rings and algebras 17B01 Identities, free Lie (super)algebras 16R40 Identities other than those of matrices over commutative rings 17C05 Identities and free Jordan structures 20C30 Representations of finite symmetric groups Keywords:polynomial identities; free algebras; T-ideals; Young diagrams; non-associative algebras; representations of symmetric groups; identities of matrices × Cite Format Result Cite Review PDF