相关论文: On the Product in Negative Tate Cohomology for Fin…

Suppose $k$ is a finite field, that $C$ is a smooth projective geometrically irreducible curve over $k$, and that $n$ is a positive integer not divisible by the characteristic of $k$. In this paper we compute cup products of elements of the…

This paper explores the cup and cap products within the cohomology and homology groups of ample groupoids, focusing on their applications and fundamental properties. Ample groupoids, which are \'etale groupoids with a totally disconnected…

Let A be any finite dimensional Hopf algebra over a field k. We specify the Tate and Tate-Hochschild cohomology for A and introduce cup products that make them become graded rings. We establish the relationship between these rings. In…

We study cup product and cap product in Tate-Hochschild theory for a finite dimensional Frobenius algebra. We show that Tate-Hochschild cohomology ring equipped with cup product is isomorphic to singular Hochschild cohomology ring…

In this note we give formulas for cup product in Tate cohomology in terms of inhomogeneous cochains. Using one of these formulas, for a torus T defined over a non-archimedean local field K and splitting over a cyclic extension of K, we…

We define a cup product on the Hochschild cohomology of an associative conformal algebra $A$, and show the cup product is graded commutative. We define a graded Lie bracket with the degree $-1$ on the Hochschild cohomology $\HH^{\ast}(A)$…

When a finite group acts linearly on a complex vector space, the natural semi-direct product of the group and the polynomial ring over the space forms a skew group algebra. This algebra plays the role of the coordinate ring of the resulting…

We interpret the complexes defining rack cohomology in terms of a certain differential graded bialgebra. This yields elementary algebraic proofs of old and new structural results for this cohomology theory. For instance, we exhibit two…

This paper concerns cup product pairings in \'etale cohomology related to work of M. Kim and of W. McCallum and R. Sharifi. We will show that by considering Ext groups rather than cohomology groups, one arrives at a pairing which combines…

Given an extension $0\to V\to G\to Q\to1$ of locally compact groups, with $V$ abelian, and a compatible essentially bijective $1$-cocycle $\eta\colon Q\to\hat V$, we define a dual unitary $2$-cocycle on $G$ and show that the associated…

We study integer-graded cohomology rings defined over Calabi-Yau categories. We show that the cohomology in negative degree is a trivial extension of the cohomology ring in non-negative degree, provided the latter admits a regular sequence…

$HC_*(A \rtimes G)$ is the cyclic homology of the crossed product algebra $A \rtimes G.$ For any $g \epsilon G$ we will define a homomorphism from $HC_*^g(A),$ the twisted cylic homology of $A$ with respect to $g,$ to $HC_*(A \rtimes G).$…

Let $G$ be a finite group, $X$ be a compact $G$-space. In this note we study the $(\mathbb{Z}_ + \times\mathbb{Z}/2\mathbb{Z})$-graded algebra $$\mathcal{F}^q_G(X) = \bigoplus_{n\geq0} q^n \cdot…

We show that the Tate-Hochschild cohomology ring $HH^*(RG,RG)$ of a finite group algebra $RG$ is isomorphic to a direct sum of the Tate cohomology rings of the centralizers of conjugacy class representatives of $G$. Moreover, our main…

We study finite group actions on Leibniz algebras, define equivariant cohomology groups associated to such actions. We show that there exists a cup-product operation on this graded cohomology groups which makes it a graded zinbiel algebra.

Viewing group cohomology as a cohomological functor, G. Mislin has generalised Tate cohomology from finite groups to all discrete groups by defining a completion for cohomological functors in 1994. In a previous paper, we have constructed…

We present an explicit description, in terms of central simple algebras, of a cup-product map which occurs in the statement of local Tate duality for Galois modules of prime order p. Given cocycles f and g, we construct a central simple…

Let $M$ be a negatively curved compact Riemannian manifold with (possibly empty) convex boundary. Every closed differential $2$-form $\xi\in\Omega^2(M)$ defines a bounded cocycle $c_\xi\in C_b^2(M)$ by integrating $\xi$ over straightened…

We define cup coproducts for Hopf cyclic cohomology of Hopf algebras and for its dual theory. We show that for universal enveloping algebras and group algebras our coproduct recovers the standard coproducts on Lie algebra homology and group…

We define a cup-product in Hom-Leibniz cohomology and show that the cup-product satisfies the graded Hom-Zinbiel relation.