U_q⁺(B₂) and its representations

2025/03/27 by Bera, Sanu, Mukherjee, Snehashis · 1 citation
#FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2503.21170

Abstract

In this article we investigate the algebra U_q⁺(B₂). Assume that q is a primitive m-th root of unity with m ≥ 5. We prove that U_q⁺(B₂) 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⁺(B₂) and we classify up to isomorphism the simple U_q⁺(B₂)-modules. We also find the center of U_q⁺(B₂).

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• Simple Modules and PI Structure of the Two-Parameter Quantized Algebra U⁺_r,s(B₂)

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