Deformations of Courant pairs and Poisson algebras

Article Type

Research Article

Publication Title

Journal of Algebra and its Applications

Abstract

We study the deformation of Courant pairs with a commutative algebra base. We consider the deformation cohomology bi-complex and describe a universal infinitesimal deformation. In a sequel, we formulate an extension of a given deformation of a Courant pair to another with extended base, which leads to describe the obstruction in extending a given deformation. We also discuss the construction of versal deformation of Courant pairs. As an application, we compute universal infinitesimal deformation of Poisson algebra structures on the three-dimensional complex Heisenberg Lie algebra. We compare the second deformation cohomology spaces of these Poisson algebra structures by considering them in the category of Leibniz pairs and Courant pairs, respectively.

DOI

10.1142/S0219498821502297

Publication Date

12-1-2021

Comments

Open Access, Green

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