On Quillen-Barr-Beck cohomology for restricted Lie algebras

Abstract: In this talk we define and study Quillen-Barr-Beck cohomology for the category of restricted Lie algebras. We prove that the first Quillen-Barr-Beck’s cohomology classifies general abelian extensions of restricted Lie algebras. Moreover, using Duskin-Glenn’s torsors cohomology theory, we prove a classification theorem for the second Quillen-Barr-Beck cohomology group in terms of 2-fold extensions of restricted Lie algebras. Finally, we give an interpretation of Cegarra-Aznar’s exact sequence for torsor cohomology.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar