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arXiv · 1505.07165

Certain Clifford-like algebra and quantum vertex algebras

Haisheng Li·Shaobin Tan·Qing Wang
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Abstract

In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$-graded irreducible modules by using a notion of Verma module. On the other hand, we introduce a new algebra, a twin of the original algebra. Using this new algebra we construct a quantum vertex algebra and we associate $\mathbb N$-graded modules for Jing-Nie's Clifford-like algebra with $ϕ$-coordinated modules for the quantum vertex algebra. We also show that the adjoint module for the quantum vertex algebra is irreducible.

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Haisheng Li, Shaobin Tan, Qing Wang. 2015-05-27. Certain Clifford-like algebra and quantum vertex algebras. https://arxiv.org/abs/1505.07165

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