# A New Cohomology Theory Associated to Deformations of Lie Algebra Morphisms

@article{Fregier2003ANC, title={A New Cohomology Theory Associated to Deformations of Lie Algebra Morphisms}, author={Yael Fregier}, journal={Letters in Mathematical Physics}, year={2003}, volume={70}, pages={97-107} }

We introduce a new cohomology theory related to deformations of Lie algebra morphisms. This notion involves simultaneous deformations of two Lie algebras and a homomorphism between them.

## 19 Citations

Morphisms Cohomology and Deformations of Hom-algebras

- MathematicsJournal of Nonlinear Mathematical Physics
- 2018

The purpose of this paper is to define cohomology complexes and study deformation theory of Hom-associative algebra morphisms and Hom-Lie algebra morphisms. We discuss infinitesimal deformations,…

Cohomology and deformations of n-Lie algebra morphisms

- Mathematics, PhysicsJournal of Geometry and Physics
- 2018

Abstract The study of n -Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper…

Simultaneous deformations of algebras and morphisms via derived brackets

- Mathematics, Physics
- 2013

We present a method to construct explicitly L-infinity algebras governing simultaneous deformations of various kinds of algebraic structures and of their morphisms. It is an alternative to the heavy…

Deformation of Dual Leibniz Algebra Morphisms

- Mathematics
- 2007

An algebraic deformation theory of morphisms of dual Leibniz algebras is obtained.

Cohomology of morphism Lie algebras and some applications

- Mathematics
- 2021

A morphism Lie algebra is a triple (g, h, φ) consisting of two Lie algebras g, h and a Lie algebra homomorphism φ : g → h. We define representations and cohomology of morphism Lie algebras. As…

Cohomology and deformations of Jacobi-Jordan algebras

- Mathematics
- 2021

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…

Cohomologies and deformations of pre-Lie-morphism triples

- Mathematics
- 2021

A (pre-)Lie-morphism triple consists of two (pre-)Lie algebras and a (pre-)Lie algebra homomorphism between them. We give chomologies of pre-Lie-morphism triples. As an application, we study the…

A pr 2 01 8 C ohomology and Deformations of n-Lie algebra morphisms

- 2018

The study of n-Lie algebras which are natural generalization of Lie algebras is motivated by Nambu Mechanics and recent developments in String Theory and M-branes. The purpose of this paper is to…

Deformations of coalgebra morphisms

- Mathematics
- 2006

An algebraic deformation theory of coalgebra morphisms is constructed.

Deformation theory of dialgebra morphisms

- Mathematics
- 2006

An algebraic deformation theory of dialgebra morphisms is obtained.

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