- This event has passed.
Samantha Kirk, NC State, How to Construct Representations of Twisted Toroidal Lie Algebras via Lattice Vertex Algebras
March 29, 2021 | 3:00 pm - 4:00 pm EDT
If you take a simple finite-dimensional Lie algebra g and tensor it with the Laurent polynomials in one variable, then you will get an infinite-dimensional Lie algebra known as a loop algebra. Affine Lie algebras are the central extensions of such loop algebras and their representations have been of interest to several mathematicians. What happens if we tensor g with the Laurent polynomials in several variables (instead of just one) and create a central extension? The result is known as a toroidal Lie algebra. I am interested in representations of certain toroidal Lie algebras that have been twisted.
In this talk, I will show how representations of twisted toroidal Lie algebras can be constructed using lattice vertex algebras. The method I will use builds on what is known about the connection between lattice vertex algebras and representations of affine Lie algebras. In fact, the only difference is I will use a bigger lattice! This talk should be approachable for students who have taken MA 720 and/or MA 725.
(Joint work with Bojko Bakalov)
Instructions: A Zoom link will be sent out to the Algebra and Combinatorics mailing list. If you would like to be added to the mailing list, please contact Corey Jones at cmjones6@ncsu.edu