Brown algebras, Freudenthal triple systems and exceptional groups over rings

Abstract: Exceptional algebraic groups are intimately related to various classes of non-associative algebras: for example, octonion algebras are related to groups of type $G_2$ and $D_4$, and Albert algebras to groups of type $F_4$ and $E_6$. This can be used, on the one hand, to give concrete descriptions of homogeneous spaces under these groups and, on the other hand, to parametrize isotopes of these algebras using said homogeneous spaces. The key tools are provided by the machinery of torsors and faithfully flat descent, working over arbitrary commutative rings (sometimes assuming 2 and 3 to be invertible).

I will talk about recent work where we do this from Brown algebras and their associated Freudenthal triple systems, whose automorphism groups are of type $E_6$ and $E_7$, respectively. I will hopefully be able to show how algebraic and geometric properties come together in this picture.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar