Seminar for Algebra, SCE QuantiXLie

On Tuesday, April 5, 2022, Gaywalee Yamskulna (Illinois State University) will give lecture as part of Seminar for Algebra titled:

"On ℕ-graded vertex algebras associated with vertex algebroids that are cyclic Leibniz algebras".

Abstract:

For an ℕ-graded vertex algebra V=⊕_n=0^{∞}V_n such that dim V₀≥ 2, it is known that V₀ is a unital commutative associative algebra, and V₁ is a Leibniz algebra. Compatibility relations on the algebraic structure of the vertex algebra V yield a beautiful structure on V₀⊕ V₁ which we call a vertex V₀-algebroid V₁. It was shown by Gorbounov, Malikov, and Schechtman that for a given vertex A-algebroid B, one can construct an ℕ-graded vertex algebra V=⊕_n=0^{∞}V_n such that V₀=A and the vertex A-algebroid V₁ is isomorphic to B. All the constructed ℕ-graded vertex algebras are generated by V₀⊕ V₁ with a spanning property of PBW type. The vertex algebra associated with a βγ system is an example of such ℕ-graded vertex algebra.  

The ℕ graded vertex algebras associated with vertex algebroids are natural and important to study. However, a classification of such ℕ-graded vertex algebras and their modules are far from being completed. In this talk, I will discuss our investigation into representation theory of vertex algebras associated with vertex algebroids that are cyclic Leibniz algebras.  

This talk is based on joint work with C. Barnes, E. Martin, G. Seelinger, and J. Service.  

Lecture beginns at  18:15 hours with Zoom stream.

Zoom:
Topic: Seminar za algebru-Gail
Time: Apr 5, 2022 06:00 PM Sarajevo, Skopje, Zagreb

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https://us02web.zoom.us/j/88497596862?pwd=SXdCVnJRY1h6WE9MK0YwVVFPZnRJdz09

Meeting ID: 884 9759 6862
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