Lie properties of symmetric elements in group rings.

DOI10.1016/j.jalgebra.2008.09.041zbMath1169.16014OpenAlexW2060503743WikidataQ115351330 ScholiaQ115351330MaRDI QIDQ1014582

Sudarshan K. Sehgal, Antonio Giambruno, Francisco César Polcino Milies

Publication date: 29 April 2009

Published in: Journal of Algebra (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1016/j.jalgebra.2008.09.041

zbMATH Keywords

group algebrasinvolutionsLie algebrassymmetric elementsskew-symmetric elementsLie nilpotenceLie \(n\)-Engel algebrasLie nilpotent algebras

Mathematics Subject Classification ID

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

Related Items (19)

Restricted enveloping algebras whose skew and symmetric elements are Lie metabelian ⋮ Group algebras and Lie nilpotence. ⋮ Oriented group involutions in group algebras: a survey ⋮ Lie identities on symmetric elements of restricted enveloping algebras ⋮ Star-group identities on units of group algebras: the non-torsion case ⋮ 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. ⋮ Normal group algebras ⋮ Group algebras of torsion groups and Lie nilpotence ⋮ Lie Properties of Symmetric Elements Under Oriented Involutions ⋮ A Survey on *-Group Identities on Units of Group Rings ⋮ Oriented Group Involutions and Anticommutativity in Group Rings ⋮ 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 ⋮ Lie properties of symmetric elements in group rings. II. ⋮ Group identities on symmetric units. ⋮ Group rings whose skew elements are bounded Lie Engel.

Cites Work

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