Group algebras whose symmetric and skew elements are Lie solvable

DOI10.1515/FORUM.2009.033zbMath1194.16019OpenAlexW2034787542WikidataQ115236438 ScholiaQ115236438MaRDI QIDQ5191076

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

Publication date: 28 July 2009

Published in: Forum Mathematicum (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1515/forum.2009.033

zbMATH Keywords

group algebrasinvolutionssymmetric elementsskew-symmetric elementsskew elementsLie propertiesLie solvable group rings

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 ⋮ Lie identities on symmetric elements of restricted enveloping algebras ⋮ Lie identities for skew and symmetric elements of semiprime superalgebras with superinvolution. ⋮ Bounded Engel and solvable unitary units in group rings ⋮ Skew-symmetric elements of rational group algebras ⋮ Lie derived length and involutions in group algebras. ⋮ LIE METABELIAN SKEW ELEMENTS IN GROUP RINGS ⋮ On the Lie algebra of skew-symmetric elements of an enveloping algebra ⋮ Lie properties of symmetric elements in group rings. II. ⋮ COMMUTATOR IDENTITIES ON SYMMETRIC ELEMENTS OF GROUP ALGEBRAS ⋮ Additive mappings and identities on unit groups of algebraic algebras

Cites Work

• Groups whose irreducible representations have degree at most 2.
• Unitary units and skew elements in group algebras.
• On the Lie structure of an associative ring
• Lie nilpotence of group rings
• Group rings whose symmetric elements are Lie nilpotent
• The lien-engel property in group rings
• Symmetric Elements Under Oriented Involutions in Group Rings
• Lie Solvable Group Rings

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