Let F be a field. A Symplectic alternating algebra over F is a triple (V, ( , ), · ) where V is a symplectic vector space over F with respect to a non-degenerate alternating form ( , ) and · is an alternating bilinear and binary operation on V 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.
Nilpotent Symplectic Alternating Algebras
Layla Sorkatti, Southern Illinois University
2022 AWM Research Symposium