Derivations, extensions, and rigidity of subalgebras of the Witt algebra

Abstract: We study Lie algebraic properties of subalgebras of the Witt algebra and the one-sided Witt algebra: we compute derivations, one-dimensional extensions, and automorphisms of these subalgebras. In particular, all these properties are inherited from the full Witt algebra (e.g. derivations of subalgebras are simply restrictions of derivations of the Witt algebra). We also prove that any isomorphism between subalgebras of finite codimension extends to an automorphism of the Witt algebra. We explain this "rigid" behavior by proving a universal property satisfied by the Witt algebra as a completely non-split extension of any of its subalgebras of finite codimension. This is a purely Lie algebraic property which I will introduce in the talk.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar