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Let $G$ be a complex, connected, reductive algebraic group. In this paper we show analogues of the computations by Borho and MacPherson of the invariants and anti-invariants of the cohomology of the Springer fibres of the cone of nilpotent…

Let $K$ be an arbitrary infinite field. The cohomology group $H^2(SL(2,K), H_2\,SL(2,K))$ contains the class of the universal central extension. When studying representations of fundamental groups of surfaces in $SL(2,K)$ it is useful to…

The C*-algebras called Quantum Heisenberg Manifolds (QHM) were introduced by Rieffel in 1989 as strict deformation quantizations of Heisenberg manifolds. In this article, we compute the pairings of K-theory and cyclic cohomology on the QHM.…

We compute the Hochschild cohomology of universal enveloping algebras of Lie-Rinehart algebras in terms of the Poisson cohomology of the associated graded quotient algebras. Central in our approach are two cochain complexes of "nonlinear…

This paper introduces the notion of locally algebraic representations and corresponding sheaves in the context of the cohomology of arithmetic groups. These representations are of relevance for the study of integral structures and special…

Given a smooth projective variety $X$ over a field $k$ of characteristic zero, we consider the composition of the de Rham cohomology cycle class map over $k$ from the Chow group $CH^q(X\times_kK)$, where $K$ is the field of fractions of…

We study the arithmetic of degree $N-1$ Eisenstein cohomology classes for locally symmetric spaces associated to $\mathrm{GL}_N$ over an imaginary quadratic field $k$. Under natural conditions we evaluate these classes on $(N-1)$-cycles…

We show by a direct computation that, for any Hopf algebra with a modulus-like character, the formulas first introduced in [CM] in the context of characteristic classes for actions of Hopf algebras, do define a cyclic module. This provides…

We study a Hopf algebroid, $\calh$, naturally associated to the groupoid $U_n^\delta\ltimes U_n$. We show that classes in the Hopf cyclic cohomology of $\calh$ can be used to define secondary characteristic classes of trivialized flat…

The representation theory of 0-Hecke-Clifford algebras as a degenerate case is not semisimple and also with rich combinatorial meaning. Bergeron et al. have proved that the Grothendieck ring of the category of finitely generated…

This paper exhibits a multiplicative and minimal cellular complex which allows explicit and complete (co)homological calculations for the symmetric products of a finite two dimensional CW complex. By considering cohomology, we observe that…

The problem of computing the integral cohomology ring of the symmetric square of a topological space has been of interest since the 1930s, but limited progress has been made on the general case until recently. In this work we offer a…

The general construction of self-adjoint configuration space representations of the Heisenberg algebra over an arbitrary manifold is considered. All such inequivalent representations are parametrised in terms of the topology classes of flat…

In a previous paper, the author compute the dimension of Hochschild cohomology groups of Jacobian algebras from (unpunctured) triangulated surfaces, and gave a geometric interpretation of those numbers in terms of the number of internal…

Let $A$ be a Hopf algebra over a field $K$ of characteristic 0 and suppose there is a coalgebra projection $\pi$ from $A$ to a sub-Hopf algebra $H$ that splits the inclusion. If the projection is $H$-bilinear, then $A$ is isomorphic to a…

We define transalgebraic functions on a compact Riemann surface as meromorphic functions except at a finite number of punctures where they have finite order exponential singularities. This transalgebraic class is a topological…

Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…

The subject of the present work is the de Rham part of non-commutative Hodge structures on the periodic cyclic homology of differential graded algebras and categories. We discuss explicit formulas for the corresponding connection on the…

The topology of periodic spaces has attracted a lot of interest in recent years in order to study and classify crystalline structures and other large homogeneous data sets, such as the distribution of galaxies in cosmology. In practice,…

Real Clifford algebras play a fundamental role in the eight real Altland-Zirnbauer symmetry classes and the classification tables of topological phases. Here, we present another elegant realization of real Clifford algebras in the…