Related papers: Cyclic Cohomology of the Weyl Algebra
Our aim in this paper is to investigate the first Hochschild cohomology of {\em admissible algebras} which can be seen as a generalization of basic algebras. For this purpose, we study differential operators on an admissible algebra.…
Relying of properties of the inductive tensor product, we construct cyclic type homology theories for certain nuclear algebras. In this context we establish continuity theorems. We compute the periodic cyclic homology of the Schwartz…
A cohomology theory of the adjoint of Hopf algebras, via deformations, is presented by means of diagrammatic techniques. Explicit calculations are provided in the cases of group algebras, function algebras on groups, and the bosonization of…
Huayi Chen introduces the notion of an approximable graded algebra, which he uses to prove a Fujita-type theorem in the arithmetic setting, and asked if any such algebra is the graded ring of a big line bundle on a projective variety. This…
We set up a homological algebra for N-complexes, which are graded modules together with a degree -1 endomorphism d satisfying d^N=0. We define Tor- and Ext-groups for N-complexes and we compute them in terms of their classical counterparts…
The study of Cowen-Douglas operators involves not only operator-theoretic tools but also complex geometry on holomorphic vector bundles. By leveraging the properties of holomorphic vector bundles, this paper investigates the cyclicity of…
We establish duality results for the cohomology of the Weil group of a $p$-adic field, analogous to, but more general than, results from Galois cohomology. We prove a duality theorem for discrete Weil modules, which implies Tate-Nakayama…
We compute the Hochschild Cohomology of a finite-dimensional preprojective algebra of generalized Dynkin type Ln over a field of characteristic different from 2 . In particular, we describe the ring structure of the Hochschild Cohomology…
Let $(\mathcal{C}, \otimes)$ be a monoidal dg-category. We construct a complex controlling the deformation of the monoidal structure on $\mathcal{C}$ together with the deformation of the underlying dg-category itself. We show that in the…
We describe explicitly the cohomology of the total complex of certain diagrams of invertible sheaves on normal toric varieties. These diagrams, called wheels, arise in the study of toric singularities associated to dimer models. Our main…
We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology…
We obtain a mixed complex simpler than the canonical one the computes the type cyclic homologies of a crossed product with invertible cocycle $A\times_{\rho}^f H$, of a weak module algebra $A$ by a weak Hopf algebra $H$. This complex is…
We discuss several seemingly assorted objects: the umbral calculus, generalised translations and associated transmutations, symbolic calculus of operators. The common framework for them is representations of the Weyl algebra of the…
We compute the cohomology with trivial coefficients of two graded infinite-dimensional Lie algebras of maximal class, give explicit formulas for their representative cocycles. Also we discuss the relations with combinatorics and…
We obtain a mixed complex, simpler that the canonical one, given the Hochschild, cyclic, negative and periodic homology of a crossed product E=A#fH, where H is an arbitrary Hopf algebra and f is a convolution invertible cocycle with values…
In this paper one considers three homotopy functors on the category of manifolds, $hH^\ast, cH^\ast, sH^\ast,$ and parallel them with other three homotopy functors on the category of connected commutative differential graded algebras,…
We realise the cohomology ring of a flag manifold, more generally the coinvariant algebra of an arbitrary finite Coxeter group W, as a commutative subalgebra of a certain Nichols algebra in the Yetter-Drinfeld category over W. This gives a…
By a result of Gerstenhaber and Schack the simplicial cohomology ring $H^*(\mathcal{C};k)$ of a poset $\mathcal{C}$ is isomorphic to the Hochschild cohomology ring $HH^*(k\mathcal{C})$ of the category algebra $k\mathcal{C}$, where the poset…
In a paper by the authors, the associative and the Lie algebras of Weyl type $A[D]=A\otimes F[D]$ were introduced, where $A$ is a commutative associative algebra with an identity element over a field $F$ of any characteristic, and $F[D]$ is…
We show that induction and restriction functors for inclusions of nilCoxeter algebras provide a categorical realization of the algebra of polynomial differential operators in one variable.