Dirac operators and the Very Strange Formula for Lie superalgebras
Victor G. Kac, Pierluigi Moseneder Frajria, Paolo Papi
TL;DR
This paper introduces a super-affine Dirac operator approach to establish a novel strange formula for quadratic Lie superalgebras with reductive even parts.
Contribution
It presents a new proof of the strange formula using a super-affine Kostant's cubic Dirac operator for Lie superalgebras.
Findings
Proves a new strange formula for Lie superalgebras.
Develops a super-affine version of Kostant's Dirac operator.
Connects Dirac operators with structural formulas in superalgebra theory.
Abstract
Using a super-affine version of Kostant's cubic Dirac operator, we prove a very strange formula for quadratic finite-dimensional Lie superalgebras with a reductive even subalgebra.
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