# Monster Lie Algebra: Friend or Foe?

### APA

Khaqan, M. (2023). Monster Lie Algebra: Friend or Foe?. Perimeter Institute. https://pirsa.org/23110089

### MLA

Khaqan, Maryam. Monster Lie Algebra: Friend or Foe?. Perimeter Institute, Nov. 30, 2023, https://pirsa.org/23110089

### BibTex

@misc{ pirsa_PIRSA:23110089, doi = {10.48660/23110089}, url = {https://pirsa.org/23110089}, author = {Khaqan, Maryam}, keywords = {Mathematical physics}, language = {en}, title = { Monster Lie Algebra: Friend or Foe?}, publisher = {Perimeter Institute}, year = {2023}, month = {nov}, note = {PIRSA:23110089 see, \url{https://pirsa.org}} }

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