Results 1 to 10 of about 78,455 (75)

Cohomology and deformations of compatible Hom-Lie algebras [PDF]

, 2022
In this paper, we consider compatible Hom-Lie algebras as a twisted version of compatible Lie algebras. Compatible Hom-Lie algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie algebras generalizing the recent work of Liu, Sheng and Bai.
arxiv   +1 more source

On the compatibility of quantum instruments [PDF]

Phys. Rev. A 105, 052202 (2022), 2021
Incompatibility of quantum devices is a useful resource in various quantum information theoretical tasks, and it is at the heart of some fundamental features of quantum theory. While the incompatibility of measurements and quantum channels is well-studied, the incompatibility of quantum instruments has not been explored in much detail. In this work, we
arxiv   +1 more source

Compatible $L_\infty$-algebras [PDF]

arXiv, 2021
A compatible $L_\infty$-algebra is a graded vector space together with two compatible $L_\infty$-algebra structures on it. Given a graded vector space, we construct a graded Lie algebra whose Maurer-Cartan elements are precisely compatible $L_\infty$-algebra structures on it.
arxiv  

On deformation cohomology of compatible Hom-associative algebras [PDF]

arXiv, 2022
In this paper, we consider compatible Hom-associative algebras as a twisted version of compatible associative algebras. Compatible Hom-associative algebras are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-associative algebras generalizing the classical ...
arxiv  

$L_\infty$-structures and cohomology theory of compatible $\mathcal {O}$-operators and compatible dendriform algebras [PDF]

arXiv, 2022
The notion of $\mathcal{O}$-operator is a generalization of the Rota-Baxter operator in the presence of a bimodule over an associative algebra. A compatible $\mathcal{O}$-operator is a pair consisting of two $\mathcal{O}$-operators satisfying a compatibility relation.
arxiv  

Deformations and abelian extensions of compatible pre-Lie algebras [PDF]

arXiv, 2023
In this paper, we first give the notation of a compatible pre-Lie algebra and its representation. We study the relation between compatible Lie algebras and compatible pre-Lie algebras. We also construct a new bidifferential graded Lie algebra whose Maurer-Cartan elements are compatible pre-Lie structures.
arxiv  

On compatible Lie and pre-Lie Yamaguti algebras [PDF]

arXiv, 2023
This study aims to generalize the notion of compatible Lie algebras to the compatible Lie Yamaguti algebras. Along with describing the representation of the compatible Lie Yamaguti algebra in detail, we also introduce the Maurer-Cartan characterization and cohomology of Lie Yamaguti algebras.
arxiv  

Cohomology of compatible BiHom-Lie algebras [PDF]

arXiv, 2023
This paper defines compatible BiHom-Lie algebras by twisting the compatible Lie algebras by two linear commuting maps. We show the characterization of compatible BiHom-Lie algebra as a Maurer-Cartan element in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible BiHom-Lie algebras.
arxiv  

On compatible Leibniz algebras [PDF]

arXiv, 2023
In this paper, we study compatible Leibniz algebras. We characterize compatible Leibniz algebras in terms of Maurer-Cartan elements of a suitable differential graded Lie algebra. We define a cohomology theory of compatible Leibniz algebras which in particular controls a one-parameter formal deformation theory of this algebraic structure. Motivated by a
arxiv  

On compatible Hom-Lie triple systems [PDF]

arXiv, 2023
In this paper, we consider compatible Hom-Lie triple systems. Compatible Hom-Lie triple systems are characterized as Maurer-Cartan elements in a suitable bidifferential graded Lie algebra. We also define a cohomology theory for compatible Hom-Lie triple systems.
arxiv