Search results for "Lie nilpotent"

showing 2 items of 2 documents

Group algebras and Lie nilpotence

2013

Abstract Let ⁎ be an involution of a group algebra FG induced by an involution of the group G. For char F ≠ 2 , we classify the groups G with no 2-elements and with no nonabelian dihedral groups involved whose Lie algebra of ⁎-skew elements is nilpotent.

Discrete mathematicsPure mathematicsAlgebra and Number TheorySimple Lie group010102 general mathematicsMathematics::Rings and AlgebrasUniversal enveloping algebra0102 computer and information sciencesGroup algebraSkew-symmetric element01 natural sciencesRepresentation theoryLie conformal algebraGraded Lie algebraRepresentation of a Lie groupgroup algebra unit010201 computation theory & mathematicsLie nilpotentGroup algebra0101 mathematicsNilpotent groupANÉIS E ÁLGEBRAS ASSOCIATIVOSMathematicsJournal of Algebra
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Lie properties of symmetric elements in group rings

2009

Abstract Let ∗ be an involution of a group G extended linearly to the group algebra KG . We prove that if G contains no 2-elements and K is a field of characteristic p ≠ 2 , then the ∗-symmetric elements of KG are Lie nilpotent (Lie n -Engel) if and only if KG is Lie nilpotent (Lie n -Engel).

Pure mathematicsAdjoint representation010103 numerical & computational mathematicsCentral series01 natural sciencesGraded Lie algebraMathematics::Group TheoryRepresentation of a Lie groupGroup ring LieLie nilpotentGroup algebra0101 mathematicsMathematics::Representation TheoryMathematicsDiscrete mathematicsAlgebra and Number TheorySimple Lie groupTEORIA DOS GRUPOSMathematics::Rings and Algebras010102 general mathematicsLie conformal algebraAdjoint representation of a Lie algebraLie n-EngelNilpotent groupSymmetric element
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