Related papers: Chiral Equivariant Cohomology II

We review cohomology theories corresponding to the chiral and classical operads. The first one is the cohomology theory of vertex algebras, while the second one is the classical cohomology of Poisson vertex algebras (PVA), and we construct…

Attached to a weight space in an integrable highest weight representation of a simply-laced Kac-Moody algebra $\mathfrak{g}$, there are two natural commutative algebras: the cohomology ring of a quiver variety and the center of a cyclotomic…

We propose a way of computing 4-manifold invariants, old and new, as chiral correlation functions in half-twisted 2d $\mathcal{N}=(0,2)$ theories that arise from compactification of fivebranes. Such formulation gives a new interpretation of…

We define a new type of Hall algebras associated e.g. with quivers with polynomial potentials. The main difference with the conventional definition is that we use cohomology of the stack of representations instead of constructible sheaves…

In a previous paper, we have constructed, for an arbitrary Lie group G and any of the fields F=R or C, a good equivariant cohomology theory KF_G^*(-) on the category of proper $G$-CW-complex and have justified why it deserved the label…

This paper explores the sheaves with the action of a lie algebra and computes their cohomology in a new category. Then in the following sections, We try to generalize a classical result in [GM, Ch. IV] about exterior algebra. We add the…

For a triple $(G,A,\kappa)$ (where $G$ is a group, $A$ is a $G$-module and $\kappa:G^3\to A$ is a 3-cocycle) and a $G$-module $B$ we introduce a new cohomology theory $_2H^n(G,A,\kappa;B)$ which we call the secondary cohomology. We give a…

We study partial homology and cohomology from ring theoretic point of view via the partial group algebra $\mathbb{K}_{par}G$. In particular, we link the partial homology and cohomology of a group $G$ with coefficients in an irreducible…

In this paper, we develop a cohomology theory of a left-symmetric conformal algebra and study its some applications. We define the cohomology of a left-symmetric conformal algebra, and then give an isomorphism between the cohomology spaces…

This survey article on relative homological algebra in bivariant K-thoery is mainly intended for readers with a background knowledge in triangulated categories. We briefly recall the general theory of relative homological algebra in…

We present an axiomatic frame (in Prt I of this book) in which many results of the K-theory for C*-algebras are proved. Then we construct an example for this axiomatic theory (in Part II), which generalizes the classical theory for…

This paper focuses on the study of a new category of vector bundles. The objects of this category, called chiral vector bundles, are pairs given by a complex vector bundle along with one of its automorphisms. We provide a classification for…

The quantum cohomology algebra of a projective manifold X is the cohomology H(X,Q) endowed with a different algebra structure, which takes into account the geometry of rational curves in X. We show that this algebra takes a remarkably…

Various aspects of orbifolds and cosets of the small $\mathcal{N}=4$ superconformal algebra are studied. First, we determine minimal strong generators for generic and specific levels. As a corollary, we obtain the vertex algebra of global…

Given a complex reductive group $G$ and a $G$-representation $\mathbf{N}$, there is an associated Coulomb branch algebra $\mathcal{A}_{G,\mathbf{N}}^\hbar$ defined by Braverman, Finkelberg and Nakajima. In this paper, we provide a new…

We extend the theorem of Hausel and the author from arXiv:2212.11836 that relates equivariant cohomology rings and algebras of functions on zero schemes. This paper combines three separate results. We prove that for a reductive group G…

We construct and study some vertex theoretic invariants associated to Poisson varieties, specialising in the conformal weight $0$ case to the familiar package of Poisson homology and cohomology. In order to do this conceptually we sketch a…

In math.RT/0302174 we developed a framework to study representations of groups of the form $G((t))$, where $G$ is an algebraic group over a local field $K$. The main feature of this theory is that natural representations of groups of this…

Given a two-dimensional quantum field theory with (0,2) supersymmetry, one can construct a chiral (or vertex) algebra. The chiral algebra of a (0,2) supersymmetric sigma model is, perturbatively, the cohomology of a sheaf of chiral…

Let G be a compact, connected Lie group, acting smoothly on a manifold M. Goresky-Kottwitz-MacPherson described a small Cartan model for the equivariant cohomology of M, quasi-isomorphic to the standard Cartan complex of equivariant…