Cohomology of Jordan triples via Lie
                    algebras

Chu, Cho-Ho; Russo, Bernard

doi:10.1090/conm/672/13465

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2021

2023

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Cited by 2 publications

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“…Our main upshot in this work is developing a cohomology and deformation theory for Jacobi-Jordan algebras analogous to the existing theories for associative and Lie algebras. Notice that there is no general cohomology for Jordan algebras, even though there is some attempts, see [9,10,17,18]. However, we introduce a cohomology that has several properties not enjoyed by the Hochschild theory.…”

Section: Introductionmentioning

confidence: 99%

Cohomology and deformations of Jacobi-Jordan algebras

Baklouti,

Benayadi,

Makhlouf

et al. 2021

Preprint

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In this paper, we define and develop a cohomology and deformation theories of Jacobi-Jordan algebras. We construct a cohomology based on two operators, called zigzag cohomology, and detail the low degree cohomology spaces. We describe the relationships between first and second cohomology groups with extensions and deformations. Moreover, we consider cohomology properties of pseudo-euclidean Jacobi-Jordan algebras and provide a deformation theory that fits with our zigzag cohomology of Jacobi-Jordan algebras. Furthermore, the paper includes several examples and applications.

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Section: Introductionmentioning

confidence: 99%