Quantized enveloping superalgebra of type $P$

Abstract

We introduce a new quantized enveloping superalgebra ${\mathfrak{U}}_q{\mathfrak{p}}_n$ attached to the Lie superalgebra ${\mathfrak{p}}_n$ of type $P$. The superalgebra ${\mathfrak{U}}_q{\mathfrak{p}}_n$ is a quantization of a Lie bisuperalgebra structure on ${\mathfrak{p}}_n$ and we study some of its basic properties. We also introduce the periplectic $q$-Brauer algebra and prove that it is the centralizer of the ${\mathfrak{U}}_q{\mathfrak{p}}_n$-module structure on $\mathbb{C}(n|n{)}^{\otimes l}$. We end by proposing a definition for a new periplectic $q$-Schur superalgebra.

14 pages, minor corrections to the earlier version

References in corpus (1)

• On representations of the Lie superalgebra p(n)

Cited by in corpus (2)

• On the Harish-Chandra Homomorphism for Quantum Superalgebras
• Webs of Type P