相关论文: Partition complexes, duality and integral tree rep…

We construct a duality functor on the category of continuous representations of linearly compact Lie superalgebras, using representation theory of Lie conformal superalgebras. We compute the dual representations of the generalized Verma…

We study the cohomology of Lie superalgebras for the full complex of forms: superforms, pseudoforms and integral forms. We use the technique of spectral sequences to abstractly compute the Chevalley-Eilenberg cohomology. We first focus on…

We consider discontinuous operations of a group $G$ on a contractible $n$-dimensional manifold $X$. Let $E$ be a finite dimensional representation of $G$ over a field $k$ of characteristics 0. Let $\mathcal{E}$ be the sheaf on the quotient…

A cohomology theory, associated to a $n$-Lie algebra and a representation space of it, is introduced. It is observed that this cohomology theory is qualified to encode the generalized derivation extensions, and that it coincides, for $n=3$,…

It is known that Hochschild cohomology groups are represented by crossed extensions of associative algebras. In this paper, we introduce crossed $n$-fold extensions of a Lie algebra $\mathfrak{g}$ by a module $M$, for $n \geq 2$. The…

This paper continues the study of the poset of eigenspaces of elements of a unitary reflection group (for a fixed eigenvalue), which was commenced in [6] and [5]. The emphasis in this paper is on the representation theory of unitary…

This paper describes the homology of various simplicial complexes associated to set families from combinatorial number theory, including primitive sets, pairwise coprime sets, product-free sets, and coprime-free sets. We present a condition…

We calculate the homology of three families of 2-step nilpotent Lie (super)algebras associated with the symplectic, orthogonal, and general linear groups. The symplectic case was considered by Getzler and the main motivation for this work…

We compute the cohomology with trivial coefficients of Lie algebras $\mathfrak{m}_0$ and $\mathfrak{m}_2$ of maximal class over the field $\mathbb{Z}_2$. In the infinite-dimensional case, we show that the cohomology rings…

We introduce a double complex that can be associated to certain Lie algebras, and show that its cohomology determines an obstruction to the existence of a half-flat SU(3)-structure. We obtain a classification of the 6-dimensional…

Let $T(n,m)$ be the set of all plane labelled bipartite trees with $n$ white vertices and $m$ black. If the number $n+m$ of vertices is even, then the set $T(n,m)$ is a union of two disjoint subsets --- subset od "even" trees and subset of…

Following our approach to metric Lie algebras developed in math.DG/0312243 we propose a way of understanding pseudo-Riemannian symmetric spaces which are not semi-simple. We introduce cohomology sets (called quadratic cohomology) associated…

Let F* be the finite field of q elements and let P(n,q) be the projective space of dimension n-1 over F*. We construct a family H^{n}_{k,i} of combinatorial homology modules associated to P(n,q) over a coefficient field F field of…

There are three kinds of Lie superalgebras for each differentiable manifold. In this note, we shall show an application of the homology groups of those superalgebras in order to classify 4 dimensional Engel-like Lie algebras.

A morphism Lie algebra is a triple $(\mathfrak{g}, \mathfrak{h}, \phi)$ consisting of two Lie algebras $\mathfrak{g}, \mathfrak{h}$ and a Lie algebra homomorphism $\phi : \mathfrak{g} \rightarrow \mathfrak{h}$. We define representations and…

We describe an explicit semi-algebraic partition for the complement of a real hyperplane arrangement such that each piece is contractible and so that the pieces form a basis of Borel-Moore homology. We also give an explicit correspondence…

If a (possibly finite) compact Lie group acts effectively, locally linearly, and homologically trivially on a closed, simply-connected four-manifold with second Betti number at least three, then it must be isomorphic to a subgroup of S^1 x…

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…

In order to understand the structure of the cohomologies involved in the study of projectively equivariant quantizations, we introduce a notion of affine representation of a Lie algebra.We show how it is related to linear representations…

We characterize finite-dimensional thick representations over ${\Bbb C}$ of connected complex semi-simple Lie groups by irreducible representations which are weight multiplicity-free and whose weight posets are totally ordered sets.…