Video URL
https://pirsa.org/23110089Monster Lie Algebra: Friend or Foe?
Maryam Khaqan Emory University
Abstract
The Monster Lie Algebra $\mathfrak m$ has two well-known avatars: It is a Borcherds' algebra that is also a quotient of the physical space of a specific tensor product of vertex algebras. In this talk, I will discuss a construction of vertex algebra elements that project to bases for subalgebras of $\mathfrak m$ isomorphic to $\mathfrak{gl}_2$, corresponding to each of the imaginary simple roots of the Monster Lie algebra.
Furthermore, for a fixed imaginary simple root, I will illustrate how the action of the Monster simple group on the Moonshine module induces an action of the Monster group on the set of the $\mathfrak{gl}_2$ subalgebras constructed this way. I will discuss this action and related open questions.
This talk is based on joint work with Darlayne Addabbo, Lisa Carbone, Elizabeth Jurisich, and Scott H. Murray.
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Zoom link TBA