The Lie superalgebra of transpositions
Representation Theory
2025-08-15 v3 Group Theory
Rings and Algebras
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.
Cite
@article{arxiv.2310.01555,
title = {The Lie superalgebra of transpositions},
author = {Christopher M. Drupieski and Jonathan R. Kujawa},
journal= {arXiv preprint arXiv:2310.01555},
year = {2025}
}
Comments
30 pages. The third version contains minor corrections that do not affect the results. The paper will appear in Algebras and Representation Theory