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.