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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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