Quasideterminants and Casimir elements for the general Lie superalgebra
Alexander Molev, Vladimir Retakh
TL;DR
This paper introduces new Casimir elements for the general Lie superalgebra using quasideterminants, linking them to supersymmetric functions via the Harish-Chandra isomorphism.
Contribution
It develops a novel method employing quasideterminants to construct Casimir elements with explicit supersymmetric function images.
Findings
Constructed new families of Casimir elements.
Connected Casimir elements to elementary, complete, and power sum supersymmetric functions.
Enhanced understanding of Lie superalgebra invariants.
Abstract
We apply the techniques of quasideterminants to construct new families of Casimir elements for the general Lie superalgebra whose images under the Harish-Chandra isomorphism are respectively the elementary, complete and power sums supersymmetric functions
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons