Mathematics

CLC number: O152.5

Presenting Little q-Schur Superalgebra u_k(2|1,3)

小q-Schur超代数 u_k(2|1,3)的展示

College of Mathematics and Physics, China Three Gorges University, Yichang 443002, Hubei, China (三峡大学　数理学院，湖北　宜昌　443002)

E-mail: This email address is being protected from spambots. You need JavaScript enabled to view it.

Received: 18 February 2025

Abstract

The purpose of this paper is to investigate the generators and relations for little q-Schur superalgebra $u_k(\mathrm{2}|\mathrm{1,3})$. The basis of $u_k(\mathrm{2}|\mathrm{1,3})$ is obtained through the Poincaré-Birkhoff-Witt (PBW) basis of q-Schur superalgebra ${\mathit{S}}_v\left(m|n,r\right)$, then we present a new set for generators and relations for $u_k(\mathrm{2}|\mathrm{1,3})$ by PBW basis.

摘要

本文研究小q-Schur超代数$u_k(\mathrm{2}|\mathrm{1,3})$的生成元与关系式。由q-Schur超代数${\mathit{S}}_v\left(m|n,r\right)$的Poincaré-Birkhoff-Witt(PBW)基得到了小q-Schur超代数$u_k(\mathrm{2}|\mathrm{1,3})$的基，并由此给出了小q-Schur超代数$u_k(\mathrm{2}|\mathrm{1,3})$一组新的生成元与关系式。