On cohomology and deformations of Jacobi-Jordan algebras
Yong Yang
TL;DR
This paper explores the cohomology and deformation theory of Jacobi-Jordan algebras, introducing methods to construct versal deformations and analyzing specific cases up to dimension 5.
Contribution
It develops a formal deformation theory for Jacobi-Jordan algebras and provides a method to construct unique versal deformations.
Findings
Constructed formal 1-parameter deformations up to dimension 5.
Developed a method for versal deformation construction.
Provided explicit versal deformations for 3-dimensional cases.
Abstract
In this paper we study cohomology and deformations of Jacobi-Jordan algebras. We develop their formal deformation theory. In particular, we introduce a method to construct a versal deformation for a given Jacobi-Jordan algebra, which can induce all deformations and is unique on the infinitesimal level. We construct formal 1-parameter deformations of Jacobi-Jordan algebras up to dimension 5 and versal deformations for 3-dimensional Jacobi-Jordan algebras.
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Taxonomy
TopicsAdvanced Topics in Algebra · Homotopy and Cohomology in Algebraic Topology · Ophthalmology and Eye Disorders