Monster Lie Algebra: Friend or Foe?

          @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}}
          }
          

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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