I will start the talk with the classical Cayley transform for the special orthogonal group SO(n) defined by Arthur Cayley in 1846. A connected linear algebraic group G over a field K is called a Cayley group if it admits a Cayley map, that is, a G-equivariant birational isomorphism between the group variety G and its Lie algebra Lie(G). For example, SO(n) is a Cayley group. A linear algebraic group G is called stably Cayley if G x (K*)^r is Cayley for some natural number r. I will consider semisimple […]

Let W be a finite dimensional algebraic structure over a field K of characteristic zero (for example an algebra or a graded algebra). In this talk I will explain how to construct a symmetric monoidal category CW which is (up to some categorical data) a complete invariant of W. This category will be a form of RepK-G, where G is the algebraic group of automorphisms of W, over some subfield K0 of K. The field K0 can be thought of as the field of invariants of W, in a way […]