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Journal Article

Quantized enveloping superalgebra of type $P$

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Grantcharov,  Dimitar
Max Planck Institute for Mathematics, Max Planck Society;

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2101.09800.pdf
(Preprint), 214KB

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Citation

Ahmed, S., Grantcharov, D., & Guay, N. (2021). Quantized enveloping superalgebra of type $P$. Letters in Mathematical Physics, 111(3): 84. doi:10.1007/s11005-021-01424-y.


Cite as: http://hdl.handle.net/21.11116/0000-0008-F42B-5
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.