Griess-like algebras for finite groups
Sergey Shpectorov

The Griess algebra is a commutative non-associative algebra
of dimension 196884 whose automorphism group is the sporadic
simple group M, the Monster. In a joint project with A.A. Ivanov
we are trying to explain some of the mysteries of the Monster
and Griess algebra, building on a recent result of Sakuma,
who classified all algebras generated by two idempotents
under additional conditions as in the Griess algebra.
  After explaining the setup, I will review Sakuma's results
and match them with certain actions of dihedral groups.
I will also demonstrate that they can be extended to further
classes of groups.