On cohomology and deformations of Jacobi-Jordan algebras

2022/02/05 by Yang, Yong
#14B12 #17C10 #Commutative Algebra (math.AC) #FOS: Mathematics #Representation Theory (math.RT)

paper · doi:10.48550/arxiv.2202.02573

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.

Related

• Cohomology and deformations of Jacobi-Jordan algebras
• Cohomologies and linear deformations of pre-Jacobi-Jordan algebras
• Versal Deformations and Versality in Central Extensions of Jacobi's Schemes
• Cohomologies and linear deformations of relative Rota-Baxter operators on (pre-)Jacobi-Jordan algebras
• Versal deformation theory of algebras over a quadratic operad