On cohomology and deformations of Jacobi-Jordan algebras

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.

Keywords:

• Cohomology
• formal deformation
• Jacobi-Jordan algebra

2020 Mathematics Subject Classification:

• 14B12
• 17C10

Acknowledgments

The author would like to thank the Doctoral School of Physics, University of Pécs for support, and Prof. Alice Fialowski for giving the problem and regular useful discussions. The author also thanks the referee for the suggestions which improved the presentation.

Disclosure statement

The author declares that there are no conflicts of interests.