Quantized enveloping superalgebra of type $P$
| Autor: | Nicolas Guay, Dimitar Grantcharov, Saber Ahmed |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2021 |
| Předmět: |
Physics
010102 general mathematics Mathematics::Rings and Algebras Quantum algebra Statistical and Nonlinear Physics Lie superalgebra Type (model theory) 01 natural sciences Centralizer and normalizer Representation theory Superalgebra Combinatorics Quantization (physics) Mathematics::Quantum Algebra 0103 physical sciences Mathematics - Quantum Algebra FOS: Mathematics Quantum Algebra (math.QA) 010307 mathematical physics 0101 mathematics Algebra over a field Representation Theory (math.RT) Mathematics::Representation Theory Mathematical Physics Mathematics - Representation Theory |
| Zdroj: | Letters in Mathematical Physics |
| Popis: | 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 |
| Databáze: | OpenAIRE |
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