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Presenting queer Schur superalgebras. (English) Zbl 1395.20032
Summary: 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 analog of the queer Schur superalgebra and investigate the presentation problem for both the queer Schur superalgebra and its quantum analog.

MSC:
20G43 Schur and \(q\)-Schur algebras
17B37 Quantum groups (quantized enveloping algebras) and related deformations
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