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Your search keyword '"Tan, Shaobin"' showing total 8 results
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8 results on '"Tan, Shaobin"'

1. Quantum vertex algebra associated to quantum toroidal $\mathfrak{gl}_N$

Author

Chen, Fulin, Huang, Xin, Kong, Fei, and Tan, Shaobin

Subjects
Mathematics - Quantum Algebra
Abstract

In this paper, we associate the quantum toroidal algebra $\mathcal{E}_N$ of type $\mathfrak{gl}_N$ with quantum vertex algebra through equivariant $\phi$-coordinated quasi modules. More precisely, for every $\ell\in \mathbb{C}$, by deforming the universal affine vertex algebra of $\mathfrak{sl}_\infty$, we construct an $\hbar$-adic quantum $\Z$-vertex algebra $V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$. Then we prove that the category of restricted $\mathcal{E}_N$-modules of level $\ell$ is canonically isomorphic to that of equivariant $\phi$-coordinated quasi $V_{\widehat{\mathfrak{sl}}_{\infty},\hbar}(\ell,0)$-modules.

Published
2024

5. Deforming vertex algebras by vertex bialgebras.

Author

Jing, Naihuan, Kong, Fei, Li, Haisheng, and Tan, Shaobin

Subjects
ALGEBRA, VERTEX operator algebras
Abstract

This is a continuation of a previous study initiated by the third author on nonlocal vertex bialgebras and smash product nonlocal vertex algebras. In this paper, we study a notion of right H -comodule nonlocal vertex algebra for a nonlocal vertex bialgebra H and give a construction of deformations of vertex algebras with a right H -comodule nonlocal vertex algebra structure and a compatible H -module nonlocal vertex algebra structure. We also give a construction of ϕ -coordinated quasi modules for smash product nonlocal vertex algebras. As an example, we give a family of quantum vertex algebras by deforming the vertex algebras associated to non-degenerate even lattices. [ABSTRACT FROM AUTHOR]

Published
2024
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6. Twisted toroidal Lie algebras and Moody-Rao-Yokonuma presentation

Author

Chen, Fulin, Jing, Naihuan, Kong, Fei, and Tan, Shaobin

Abstract

Let g be a (twisted or untwisted) affine Kac-Moody algebra, and μbe a diagram automorphism of g. In this paper, we give an explicit realization for the universal central extension ĝ[μ] of the twisted loop algebra of g with respect to μ, which provides a Moody-Rao-Yokonuma presentation for the algebra ĝ[μ] when μ, is non-transitive, and the presentation is indeed related to the quantization of twisted toroidal Lie algebras.

Published
2024
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7. Verma modules for rank two Heisenberg-Virasoro algebra

Author

Li, Zhiqiang and Tan, Shaobin

Abstract

Let ⪯ be a compatible total order on the additive group ℤ2, and Lbe the rank two Heisenberg-Virasoro algebra. For any c= (c1, c2, c3, c4) ∈ℂ4, we define a ℤ2-graded Verma module M(c, ⪯) for L. A necessary and sufficient condition for M(c, ⪯) to be irreducible is provided. Moreover, the maximal ℤ2-graded submodules of M(c, ⪯) are characterized when M(c, ⪯) is reducible.

Published
2024
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8. Toroidal extended affine Lie algebras and vertex algebras.

Author

Chen, Fulin, Li, Haisheng, and Tan, Shaobin

Abstract

In this paper, we study nullity-2 toroidal extended affine Lie algebras in the context of vertex algebras and their ϕ-coordinated modules. Among the main results, we introduce a variant of toroidal extended affine Lie algebras, associate vertex algebras to the variant Lie algebras, and establish a canonical connection between modules for toroidal extended affine Lie algebras and ϕ-coordinated modules for these vertex algebras. Furthermore, by employing some results of Billig, we obtain an explicit realization of a class of irreducible modules for the variant Lie algebras. [ABSTRACT FROM AUTHOR]

Published
2024
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