Benjamin Briggs, University of Copenhagen

Title: The Lie algebra of integrable derivations

Abstract: A derivation on a finite dimensional algebra A can be thought of as an infinitesimal automorphism of A, and, in these terms, a derivation is integrable if this infinitesimal automorphism extends to a (formal) one-parameter family of automorphisms. As such these derivations are closely connected with the deformation theory of A, and the space of all integrable derivations forms an important invariant. I will talk about work with Lleonard Rubio y Degrassi in which we investigate the structure of this space. In particular, we use work of Gerstenhaber to show that they are closed under taking commutators, and therefore form a Lie algebra (which is restricted in positive characteristic). I will also present some counter-examples to questions of Linckelmann and of Farkas, Geiss and Marcos, about the structure of this Lie algebra.