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Extensions of (metric) Hom-Jacobi-Jordan algebras

Nejib Saadaoui

Abstract

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric) Hom-Jacobi algebra algebra by a representation.

Extensions of (metric) Hom-Jacobi-Jordan algebras

Abstract

The main purpose of this paper is to provide a second cohomology group of a (metric) Hom-Jacobi algebra with coefficients in a given representation. Moreover, we show that second cohomology group classifies abelian extensions of a (metric) Hom-Jacobi algebra algebra by a representation.
Paper Structure (16 sections, 39 theorems, 151 equations)

This paper contains 16 sections, 39 theorems, 151 equations.

Table of Contents

  1. Hom-Jacobi-Jordan algebras
  2. The second cohomology group of Hom-Jacobi-Jordan algebras
  3. Construction of the $2$-coboundary operator
  4. Construction of the $1$-coboundary operator
  5. Second cohomology group
  6. Representation of Hom-Jacobi-Jordan algebras
  7. Representation on V'=End(J,V)
  8. Extensions of Hom-Jacobi-Jordan algebras
  9. Classification of Low dimensional regular multiplicative solvable Hom-Jordan-Jacobi algebras
  10. Metric Hom-Jacobi-Jordan algebras
  11. Second cohomology group of metric Hom-Jacobi-Jordan-algebra
  12. Construction of a $2$-Coboundary operators for metric Hom-Jacobi-Jordan algebra
  13. Construction of a $1$-Coboundary operators for metric Hom-Jacobi-Jordan algebra
  14. Quadratic extensions
  15. Twofold extensions
  16. ...and 1 more sections

Key Result

Proposition 1.1

Any solvable Hom-Jacobi-Jordan algebra has an abelian ideal.

Theorems & Definitions (93)

  • Definition 1.1
  • Definition 1.2
  • Definition 1.3
  • Definition 1.4
  • Proposition 1.1
  • proof
  • Definition 1.5
  • Definition 2.1
  • Definition 2.2
  • Definition 2.3
  • ...and 83 more