scholarly journals VERTEX ALGEBRAS ASSOCIATED WITH ELLIPTIC AFFINE LIE ALGEBRAS

2011 ◽  
Vol 13 (04) ◽  
pp. 579-605 ◽  
Author(s):  
JIANCAI SUN ◽  
HAISHENG LI
Keyword(s):  
Lie Algebras ◽  
Vertex Algebras ◽  
Affine Lie Algebras ◽  
Quantum Vertex ◽  
Special Case

We associate what we call vertex ℂ((z))-algebras and their modules in a certain category with elliptic affine Lie algebras. To a certain extent, this association is similar to that of vertex algebras and their modules with affine Lie algebras. While the notion of vertex ℂ((z))-algebra is a special case of that of quantum vertex ℂ((z))-algebra, which was introduced and studied by one of us (Li), here we use those results on quantum vertex ℂ(z))-algebras in an essential way. In the course of this work, we also construct and exploit two families of Lie algebras which are closely related to elliptic affine Lie algebras.

scholarly journals SOME QUANTUM VERTEX ALGEBRAS OF ZAMOLODCHIKOV–FADDEEV TYPE

2009 ◽  
Vol 11 (05) ◽  
pp. 829-863 ◽  
Author(s):  
MARTIN KAREL ◽  
HAISHENG LI
Keyword(s):  
Normal Basis ◽  
Vertex Algebras ◽  
Quantum Vertex ◽  
Special Case

This is a continuation of a previous study of quantum vertex algebras of the Zamolodchikov–Faddeev type. In this paper, we focus our attention on the special case associated to diagonal unitary rational quantum Yang–Baxter operators. We prove that the associated weak quantum vertex algebras, if not zero, are irreducible quantum vertex algebras with a normal basis in a certain sense.

scholarly journals Trigonometric Lie algebras, affine Lie algebras, and vertex algebras

2020 ◽  
Vol 363 ◽  
pp. 106985
Author(s):  
Haisheng Li ◽  
Shaobin Tan ◽  
Qing Wang
Keyword(s):  
Lie Algebras ◽  
Vertex Algebras ◽  
Affine Lie Algebras

scholarly journals GENERAL BRANCHING FUNCTIONS OF AFFINE LIE ALGEBRAS

1995 ◽  
Vol 10 (10) ◽  
pp. 823-830 ◽  
Author(s):  
STEPHEN HWANG ◽  
HENRIC RHEDIN
Keyword(s):  
Lie Algebras ◽  
Simple Proof ◽  
Affine Lie Algebras ◽  
Finite Dimensional ◽  
Brst Cohomology ◽  
Special Case ◽  
Finite Dimensional Algebras ◽  
Explicit Expressions

Explicit expressions are presented for general branching functions for cosets of affine Lie algebras ĝ with respect to subalgebras ĝ′ for the cases where the corresponding finite-dimensional algebras g and g′ are such that g is simple and g′ is either simple or sums of u(1) terms. A special case of the latter yields the string functions. Our derivation is purely algebraical and has its origin in the results on the BRST cohomology presented by us earlier. We will here give an independent and simple proof of the validity of our results. The method presented here generalizes in a straightforward way to more complicated g and g′ such as sums of simple and u(1) terms.

Vertex algebras associated to the affine Lie algebras of abelian polynomial current algebras

2016 ◽  
Vol 27 (05) ◽  
pp. 1650046 ◽  
Author(s):  
Jinwei Yang
Keyword(s):  
Differential Equations ◽  
Lie Algebras ◽  
Tensor Category ◽  
Extension Property ◽  
Vertex Algebras ◽  
Affine Lie Algebras ◽  
Systems Of Differential Equations ◽  
Convergence And Extension ◽  
Logarithmic Intertwining Operators ◽  
Current Algebras

We construct a family of vertex algebras associated to the affine Lie algebra of polynomial current algebras of finite-dimensional abelian Lie algebras, along with their modules and logarithmic modules. These vertex algebras and their (logarithmic) modules are strongly [Formula: see text]-graded and quasi-conformal. We then show that matrix elements of products and iterates of logarithmic intertwining operators among these logarithmic modules satisfy certain systems of differential equations. Using these systems of differential equations, we verify the convergence and extension property needed in the logarithmic tensor category theory developed by Huang, Lepowsky and Zhang.

Vertex algebras and extended affine Lie algebras coordinated by rational quantum tori

2021 ◽  
Vol 569 ◽  
pp. 111-142
Author(s):  
Fulin Chen ◽  
Xiaoling Liao ◽  
Shaobin Tan ◽  
Qing Wang
Keyword(s):  
Lie Algebras ◽  
Vertex Algebras ◽  
Affine Lie Algebras ◽  
Quantum Tori
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