Layla Sorkatti: Symplectic Alternating Algebras

Abstract:

Let \(F\) be a field. A symplectic alternating algebra over \(F\) is a triple \((V, (\ ,\ ), \cdot)\), where \(V\) is a symplectic vector space over \(F\) with respect to a non-degenerate alternating form \((\ ,\ )\), and \(\cdot\) is an alternating bilinear operation on \(V\) such that the identity \((u \cdot v, w) = (v \cdot w, u)\) holds. These algebraic structures originated from research on powerful \(2\)-Engel \(3\)-groups, where a certain subclass with a richer structure emerged. In this talk, we will present these algebras in their own right, with a focus on recent work on their colored versions.