The Lie superalgebra of transpositions

2023/10/02 by Drupieski, Christopher M., Kujawa, Jonathan R. · 1 citation
#17B10 #20B30 #FOS: Mathematics #Group Theory (math.GR) #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.2310.01555

Abstract

We consider the group algebra of the symmetric group as a superalgebra, and describe its Lie subsuperalgebra generated by the transpositions. The updated version corrects some of the arguments made in Sections 4.5 - 4.7. The statements of the main results are unaffected.

Cited by

• Lie algebras generated by reflections in types BCD

Related

• A duality of the twisted group algebra of the symmetric group and a Lie superalgebra
• L'algebre de Lie des transpositions
• Division Algebras and Supersymmetry III
• S4-symmetry on the Tits construction of exceptional Lie algebras and superalgebras
• An analog of the classical invariant theory for Lie superlagebras. II