Thursday 10 Oct 2019Pure Mathematics Seminar: New families of axial algebras of Monster type

Prof. Sergey Shpectorov - University of Birmingham

H103 14:30-16:30


The class of axial algebras is a broad generalisation 



of Jordan algebras and the 196884-dimensional Griess 



algebra which was used to construct the Monster, the 



largest sporadic simple group. Instead of polylinear 



identities, such as the Jacobi or Jordan identity, axial algebras 



are governed by fusion rules limiting products of eigenvectors 



with respect to special idempotents called axes.



 



Until recently, the Griess algebra, its subalgebras and a small 



number of individually computed algebras were the only known 



axial algebras with Monster fusion rules. After explaining the 



basics of the axial algebras paradigm and its connections to physics 



and analysis, we will focus on the double axis construction which 



leads to a rich family of examples of algebras of Monster type.


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