Lie properties of symmetric elements in group rings. II.

DOI10.1016/j.jpaa.2008.11.027zbMath1170.16019OpenAlexW2066901180WikidataQ115345584 ScholiaQ115345584MaRDI QIDQ1008768

Ernesto Spinelli, Gregory T. Lee, Sudarshan K. Sehgal

Publication date: 30 March 2009

Published in: Journal of Pure and Applied Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jpaa.2008.11.027

zbMATH Keywords

group algebrasinvolutionsgroup ringssymmetric elementsskew-symmetric elementsLie \(n\)-Engel algebrasLie nilpotent algebrasLie properties

Mathematics Subject Classification ID

Group rings (16S34) Group rings of infinite groups and their modules (group-theoretic aspects) (20C07) Other kinds of identities (generalized polynomial, rational, involution) (16R50) Rings with involution; Lie, Jordan and other nonassociative structures (16W10)

Related Items (11)

Restricted enveloping algebras whose skew and symmetric elements are Lie metabelian ⋮ Oriented group involutions in group algebras: a survey ⋮ Lie identities on symmetric elements of restricted enveloping algebras ⋮ Anticommutativity of symmetric elements under generalized oriented involutions ⋮ Some classes of semisimple group (and loop) algebras over finite fields. ⋮ The bounded Lie Engel property on torsion group algebras. ⋮ Lie Properties of Symmetric Elements Under Oriented Involutions ⋮ Lie *-Nilpotence of Group Rings ⋮ Nilpotency of group ring units symmetric with respect to an involution. ⋮ On the Lie algebra of skew-symmetric elements of an enveloping algebra ⋮ Group rings whose skew elements are bounded Lie Engel.

Cites Work

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• Antisymmetric elements in group rings with an orientation morphism
• Observations on group rings
• Group rings whose symmetric elements are Lie nilpotent
• Group algebras whose units satisfy a group identity. II
• The lien-engel property in group rings
• Group algebras whose symmetric and skew elements are Lie solvable
• On Symmetric Elements and Symmetric Units in Group Rings
• Lie Solvable Group Rings

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