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

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

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.

Representations of a Class of Non-commutative Associative Algebras Related to the Quantum Torus

2008 ◽  
Vol 15 (02) ◽  
pp. 309-316
Author(s):  
Congfeng Ye
Keyword(s):  
Lie Algebras ◽  
Vertex Algebras ◽  
Affine Lie Algebras ◽  
Associative Algebras ◽  
Quantum Torus

In this paper, we study the representations of a class of non-commutative associative algebras AQ related to the quantum torus [Formula: see text], which is introduced by Berman, Gao and Krylyuk to study the extended affine Lie algebras. The representations of AQ are important for the study of the representations of certain “half lattice” vertex algebras.

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