Conference abstracts

Session S05 - Rings and Algebras

No date set

## Irreducible components of varieties of Jordan algebras

### María Eugenia Martin

### Universidade de São Paulo, Brazil - eugeniamartin@gmail.com

In 1968, F. Flanigan proved that every irreducible component of a variety of structure constants must carry an open subset of nonsingular points which is either the orbit of a single rigid algebra or an infinite union of orbits of algebras which differ only in their radicals.

In the context of the variety $Jor_n$ of Jordan algebras, it is known that, up to dimension four, every component is dominated by a rigid algebra. In this work, we show that the second alternative of Flanigan's theorem does in fact occur by exhibiting a component of $JorN_5$ which consists of the Zariski closure of an infinite union of orbits of five-dimensional nilpotent Jordan algebras, none of them being rigid.

Joint work with Iryna Kashuba (Universidade de São Paulo, Brazil).