相关论文: Cohomologies of Reynolds Lie algebras with derivat…

In this paper, we study Lie 2-bialgebras, with special attention to coboundary ones, with the help of the cohomology theory of $L_\infty$-algebras with coefficients in $L_\infty$-modules. We construct examples of strict Lie 2-bialgebras…

We define cohomology of associative H-pseudoalgebras, and we show that it describes module extensions, abelian pseudoalgebra extensions, and pseudoalgebra first order deformations. We describe in details the same results for the special…

All the basic cohomology groups and reduced cohomology groups of the extended Schr\"odinger-Virasoro conformal algebra with trivial coefficients are completely determined. In particular, we introduce the notion of the relative cohomology of…

We develop a global cohomology theory for number fields by offering topological cohomology groups, an arithmetical duality, a Riemann-Roch type theorem, and two types of vanishing theorem. As applications, we study moduli spaces of…

In this paper, we first discuss cohomology and a one-parameter formal deformation theory of Lie-Yamaguti algebras. Next, we study finite group actions on Lie-Yamaguti algebras and introduce equivariant cohomology for Lie-Yamaguti algebras…

We consider finite-dimensional complex Lie algebras. Using certain complex parameters we generalize the concept of cohomology cocycles of Lie algebras. A special case is generalization of 1-cocycles with respect to the adjoint…

We describe the main algebraic and geometric properties of the class of algebras introduced in [arXiv:0705.1629]. We discuss their origins in symplectic geometry and associative algebra, and the notions of cohomology and representations. We…

A LieDer pair (respectively, an AssDer pair) is a Lie algebra equipped with a derivation (respectively, an associative algebra equipped with a derivation). A couple of LieDer pair structures on a vector space are called Compatible LieDer…

This paper analyzes the second cohomology group of a linear cycle set with coefficients in an abelian group I, for linear cycle sets with commutative adjoint operation, focusing on the finite abelian case. It aims to classify extensions of…

Some results on (pre-)Jacobi-Jordan algebras and their representations are proved. Moreover, the notion of matched pairs and relative Rota-Baxter operators on these algebras are introduced and studied. The cohomology theory of relative…

The concept of Poisson cohomology groups associated with Poisson manifolds is a part of the theory of Lie superalgebras of vector fields. Therefore, we abstracted them as Poisson-like cohomology groups for general Lie superalgebras. In…

In the first section we recall some basic notions on Lie algebras. In a second time we study the algebraic variety of complex $n$-dimensional Lie algebras. We present different notions of deformations : Gerstenhaber deformations,…

We introduce a notion of oriented dialgebra and develop a cohomology theory for oriented dialgebras based on the possibility to mix the standard chain complexes computing group cohomology and associative dialgebra cohomology. We also…

Aim of this paper is to define a new type of cohomology for multiplicative Hom-Leibniz algebras which controls deformations of Hom-Leibniz algebra structure. The cohomology and the associated deformation theory for Hom-Leibniz algebras as…

In this paper, we study non-abelian extensions of strict Lie 2-algebras via the cohomology theory. A non-abelian extension of a strict Lie 2-algebra $\g$ by $\frkh$ gives rise to a strict homomorphism from $\g$ to $\SOut(\frkh)$.…

We study cohomology for classical Lie superalgebras $\mathfrak{g}$ (e.g. gl(m|n)) over the complex numbers. Using results from invariant theory, we show that there exist subsuperalgebras which detect the cohomology of $\mathfrak{g}.$…

In this paper, we give a new series of coboundary operators of Hom-Lie algebras. And prove that cohomology groups with respect to coboundary operators are isomorphic. Then, we revisit representations of Hom-Lie algebras, and generalize the…

We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare Lie algebra in various dimensions. We give complete answers for (non-extended) supersymmetry in all dimensions $\leq 11$. For…

We study formal deformations of multiplication in an operad. This closely resembles Gerstenhaber's deformation theory for associative algebras. However, this applies to various algebras of Loday-type and their twisted analogs. We explicitly…

In this paper, first we study dual representations and tensor representations of Hom-pre-Lie algebras. Then we develop the cohomology theory of Hom-pre-Lie algebras in term of the cohomology theory of Hom-Lie algebras. As applications, we…