$U_q^+(B_2)$ and its representations

Sanu Bera; Snehashis Mukherjee

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arXiv · 2503.21170

$U_q^+(B_2)$ and its representations

Sanu Bera·Snehashis Mukherjee

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Abstract

In this article we investigate the algebra $U_q^+(B_2)$. Assume that $q$ is a primitive $m$-th root of unity with $m \geq 5$. We prove that $U_q^+(B_2)$ becomes a Polynomial Identity (PI) algebra. It was previously known that for such algebras the simple modules are finite-dimensional with dimension at most the PI degree. We determine the PI degree of $U_q^+(B_2)$ and we classify up to isomorphism the simple $U_q^+(B_2)$-modules. We also find the center of $U_q^+(B_2)$.

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BibTeX RIS

Sanu Bera, Snehashis Mukherjee. 2025-03-27. $U_q^+(B_2)$ and its representations. https://arxiv.org/abs/2503.21170

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