Identical relations in Lie algebras

DOI10.1515/9783110566659zbMath1487.17001OpenAlexW4213293599MaRDI QIDQ2028709

Yu. A. Bakhturin

Publication date: 1 June 2021

Published in: De Gruyter Expositions in Mathematics (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/9783110566659

zbMATH Keywords

Hopf algebrasgraded algebrasLie algebrasfree Lie algebraspolynomial identitiesEngel Lie algebrasgraded identitiesrestricted Lie algebrasmultilinear polynomialscodimension sequencefinite basis of identitiesspecial Lie algebrasvarieties of Lie algebrasPI exponentgrowth of codimensionsfinite Lie algebrasHilpert seriesidentical relations in Lie algebrassubalgebras of free Lie algebras

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Representations of finite symmetric groups (20C30) Identities, free Lie (super)algebras (17B01) Structure theory for Lie algebras and superalgebras (17B05) Superalgebras (17A70) Solvable, nilpotent (super)algebras (17B30) Quasivarieties and varieties of groups (20E10) Research exposition (monographs, survey articles) pertaining to nonassociative rings and algebras (17-02) Rings with polynomial identity (16Rxx)

Related Items (11)

Codimension sequences and their asymptotic behavior ⋮ Some thoughts on the current state of the theory of identical relations in Lie algebras ⋮ Graded polynomial identities for the Lie algebra of upper triangular matrices of order 3 ⋮ Codimension growth of simple Jordan superalgebras ⋮ Scale for codimension growth of Poisson PI-algebras ⋮ Nilpotent algebras, implicit function theorem, and polynomial quasigroups ⋮ Representations via differential algebras and equationally Noetherian algebras ⋮ Automorphic equivalence in the classical varieties of linear algebras ⋮ Algebras with representable representations ⋮ Differential polynomial identities of upper triangular matrices under the action of the two-dimensional metabelian Lie algebra ⋮ Non-associative Algebras

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