Cohomology and deformations of Courant pairs
Ashis Mandal, Satyendra Kumar Mishra
TL;DR
This paper introduces Courant pairs, a new algebraic structure combining Courant and Leibniz algebra concepts, and explores their formal deformations using a specialized cohomology bicomplex.
Contribution
It defines Courant pairs and develops a cohomology bicomplex framework to study their formal deformations, linking Hochschild and Leibniz cohomologies.
Findings
Defined Courant pairs as Courant algebra over derivations
Constructed a cohomology bicomplex for deformations
Established connections between Hochschild and Leibniz cohomologies
Abstract
In this note we define a notion of Courant pair as a Courant algebra over the Lie algebra of linear derivations on an associative algebra. We study formal deformations of Courant pairs by constructing a cohomology bicomplex with coefficients in a module from the cochain complexes defining Hochschild cohomology and Leibniz cohomology.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Homotopy and Cohomology in Algebraic Topology