Presenting queer Schur superalgebras

TL;DR

This paper introduces the quantum analogue of queer Schur superalgebras, exploring their presentations and extending classical superalgebra concepts into the quantum setting.

Contribution

It defines the quantum queer Schur superalgebra and investigates its presentation, advancing the understanding of superalgebra structures in quantum algebra.

Findings

Defined the quantum queer Schur superalgebra.

Provided presentation results for the quantum and classical queer Schur superalgebras.

Extended superalgebra theory into the quantum domain.

Abstract

Associated to the two types of finite dimensional simple superalgebras, there are the general linear Lie superalgebra and the queer Lie superalgebra. The universal enveloping algebras of these Lie superalgebras act on the tensor spaces of the natural representations and, thus, define certain finite dimensional quotients, the Schur superalgebras and the queer Schur superalgebra. In this paper, we introduce the quantum analogue of the queer Schur superalgebra and investigate the presentation problem for both the queer Schur superalgebra and its quantum analogue.