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U_q^+(B₂) and its representations
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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 $U_q^+(B_2)$.
Forward citations
Cited by 2 Pith papers
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The PI property of skew PBW extensions
Bijective skew PBW extensions over prime PI-algebras have nontrivial centers, which determines their PI property from center descriptions.
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The PI property of skew PBW extensions
Bijective skew PBW extensions over prime PI-algebras have nontrivial centers, enabling PI property checks via center descriptions.
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