Lie prealgebras
Michel Dubois-Violette, Giovanni Landi
TL;DR
This paper introduces a generalized concept of Lie algebras within nonhomogeneous quadratic algebras, highlighting its importance in quantum group theory and connecting differential calculus with Koszul duality.
Contribution
It presents a new framework for Lie algebras in the context of nonhomogeneous quadratic algebras and relates it to quantum groups and Koszul duality.
Findings
Establishes a link between differential calculus on quantum groups and Koszul duality.
Introduces a generalized Lie algebra concept within nonhomogeneous quadratic algebras.
Highlights the relevance of this framework in quantum group theory.
Abstract
We introduce a generalization of Lie algebras within the theory of nonhomogeneous quadratic algebras and point out its relevance in the theory of quantum groups. In particular the relation between the differential calculus on quantum group and the Koszul duality due to Positselski is made apparent.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology