Related papers: Cohomology of Lie Superalgebras: Forms, Integral F…
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…
We introduce the notion of cyclic cohomology of an A-infinity algebra and show that the deformations of an A-infinity algebra which preserve an invariant inner product are classified by this cohomology. We use this result to construct some…
Let G be a reductive algebraic group over a field of prime characteristic. One can associate to G (or subgroups thereof) its Lie algebra, its Frobenius kernels, and the finite Chevalley group of points over a finite field. The…
Given a nilpotent Lie algebra $\mathfrak n$ we construct a spectral sequence which is derived from a filtration of its Chevalley-Eilenberg differential complex and converges to the Lie algebra cohomology of $\mathfrak n$. The limit of this…
In this paper, we introduce a representation theory of Hom-Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop cohomology theory of Hom-Lie conformal superalgebras and discuss some…
We study the homology and cohomology groups of super Lie algebra of supersymmetries and of super Poincare algebra. We discuss in detail the calculation in dimensions D=10 and D=6. Our methods can be applied to extended supersymmetry algebra…
The purpose of this paper is to extend the cohomology and conformal derivation theories of the classical Lie conformal algebras to Lie conformal superalgebras. Firstly, we construct the semidirect product of a Lie conformal superalgebra and…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…
Given the L-series of a half-integral weight cusp form, we construct a cohomology class with coefficients in a finite dimensional vector space in a way that parallels the Eichler cohomology in the integral weight case. We also define a lift…
Support varieties for Lie superalgebras over the complex numbers were introduced in \cite{BKN1} using the relative cohomology. In this paper we discuss finite generation of the relative cohomology rings for Lie superalgebras, we formulate a…
Using Howe duality we compute explicitly Kostant-type homology groups for a wide class of representations of the infinite-dimensional Lie superalgebra $\hat{\frak{gl}}_{\infty|\infty}$ and its classical subalgebras at positive integral…
By definition, a quadratic Lie superalgebra is a Lie superalgebra endowed with a non-degenerate supersymmetric bilinear form which satisfies the even and invariant properties. In this paper we calculate all of the second cohomology group of…
In this paper, a supersymmetric extension of a system of hydrodynamic type equations involving Riemann invariants is formulated in terms of a superspace and superfield formalism. The symmetry properties of both the classical and…
In this thesis, we introduce a new cohomology theory associated to a Lie 2-algebras and a new cohomology theory associated to a Lie 2-group. These cohomology theories are shown to extend the classical cohomology theories of Lie algebras and…
The integral singular cohomology ring of the Grassmann variety parametrizing $r$-dimensional subspaces in the $n$-dimensional complex vector space is naturally an irreducible representation of the Lie algebra of all the $n\times n$ matrices…
In this paper, we define a new cohomology theory for multiplicative Hom-pre-Lie algebras which controls deformations of Hom-pre-Lie algebra structure. This new cohomology is a natural one by considering the structure map. We develop…
A well-known and old result of Hazewinkel and Koszul states that the cohomology of a finite-dimensional Lie algebra is isomorphic, up to a suitable shift, to its twisted homology, a Lie-theoretical version of Poincare duality. This paper…
Let $(L, \alpha)$ be a Hom-Lie-Yamaguti superalgebra. We first introduce the representation and cohomology theory of Hom-Lie-Yamaguti superalgebras. Furthermore, we introduce the notions of generalized derivations and representations of…
The paper is another step towards a realisation of the goal, advanced in articles 1706.05682 [hep-th] and 1808.04470 [hep-th], of a systematic supersymmetry-equivariant geometrisation of physically distinguished Green-Schwarz…
In this paper, we extend the concept of Lie superalgebras to a more generalized framework called Super-Lie superalgebras. In addition, they seem to be exploring various supergeneralizations of other algebraic structures, such as…