Curved Koszul duality and cyclic (co)homology
Yining Zhang
TL;DR
This paper develops a curved Koszul duality framework for QLC algebras and explores its implications for cyclic (co)homology, extending classical results and applying to both associative and Lie algebra contexts.
Contribution
It introduces a new curved Koszul duality theory for QLC algebras and extends cyclic (co)homology results to this setting, including commutative and Lie analogs.
Findings
Extended Feigin-Tsygan result to curved DG algebras
Established duality for QLC algebras and their cyclic (co)homology
Analyzed curved Koszul duality in associative, commutative, and Lie cases
Abstract
We study the curved Koszul duality theory for associative algebras presented by quadratic-linear-constant (QLC) relations. As an application, we investigate the cyclic (co)homology of a QLC algebra and its Koszul dual curved DG algebra, and extend a result due to Feigin and Tsygan. We also study a commutative/Lie analog of this curved Koszul duality theory.
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Taxonomy
TopicsHomotopy and Cohomology in Algebraic Topology · Advanced Topics in Algebra · Algebraic structures and combinatorial models