Extending earlier work by Ivanov on Majorana algebras, axial algebras of Monster type were introduced in 2015 by Hall, Rehren and Shpectorov in order to axiomatize some key features of certain classes of algebras related to large families of finite simple groups, such as the weight-2 components of OZ-type vertex operator algebras, Jordan algebras, and Matsuo algebras. In this talk, I’ll review the definition of axial algebras and the major examples. Then I’ll discuss the general classification problem of the 2-generated objects and, time permitting, show its applications in some special cases related to the Monster.
This video is part of the European Non-Associative Algebra Seminar series.
