Quadratically defined Lie algebras and HNN-extension

Abstract: In this talk, we will delve into the class of Lie algebras defined by quadratic relations, focusing on the explicit computation of their cohomology rings in specific cases. These algebras naturally arise in the broader context of positively graded Lie algebras, where they play a significant structural role. The theory of HNN-extensions plays a crucial role in this context, providing a powerful tool for decomposing quadratic Lie algebras into smaller components. Moreover, we will explore how HNN-extensions can be used to embed finitely presented positively graded Lie algebras into quadratic ones.

quantum algebrarings and algebras

Audience: researchers in the topic

European Non-Associative Algebra Seminar