79. 22/07/2024 Ioannis Dokas (National and Kapodistrian University of Athens, Greece) 

Title: 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.
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