The Lie superalgebra of transpositions
Christopher M. Drupieski, Jonathan R. Kujawa
TL;DR
This paper studies the Lie subsuperalgebra generated by transpositions within the group algebra of the symmetric group viewed as a superalgebra, providing corrected arguments while maintaining core results.
Contribution
It offers a detailed description of the Lie subsuperalgebra generated by transpositions in the symmetric group algebra, with corrected proofs of key results.
Findings
Characterization of the Lie subsuperalgebra of transpositions
Corrected proofs of main theorems
Insights into the superalgebra structure of symmetric groups
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.
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Taxonomy
TopicsAdvanced Topics in Algebra · Finite Group Theory Research · Algebraic structures and combinatorial models