Symplectic Alternating Algebras

22 October 2013
Gunnar Traustason
Let F be a field. A symplectic alternating algebra over F consists of a symplectic vector space V over F with a non-degenerate alternating form that is also equipped with a binary alternating product · such that the law (u·v, w)=(v·w, u) holds. These algebraic structures have arisen from the study of 2-Engel groups but seem also to be of interest in their own right with many beautiful properties. We will give an overview with a focus on some recent work on the structure of nilpotent symplectic alternating algebras.