Related papers: Wold-type decomposition for doubly twisted left-in…
We extend our previous results on generalized Dixmier-Douady theory to graded $C^*$-algebras, as means for explicit computations of the invariants arising for bundles of ungraded $C^*$-algebras. For a strongly self-absorbing $C^*$-algebra…
We prove a decomposition theorem for the cd-index of a Gorenstein* poset analogous to the decomposition theorem for the intersection cohomology of a toric variety. From this we settle a conjecture of Stanley that the cd-index of Gorenstein*…
The Gelfand - Na\u{i}mark theorem supplies the one to one correspondence between commutative $C^*$-algebras and locally compact Hausdorff spaces. So any noncommutative $C^*$-algebra can be regarded as a generalization of a topological…
This paper establishes an extended representation theorem for unit-root VARs. A specific algebraic technique is devised to recover stationarity from the solution of the model in the form of a cointegrating transformation. Closed forms of…
The aim of the present work is to study the Riesz decomposition relative to a C*-algebra homomorphism T : A --> B. We prove that under some conditions on T, T-Riesz elements can be decomposed into the sum of almost T-null element and…
We develop a wide general theory of bilinear bi-parameter singular integrals $T$. First, we prove a dyadic representation theorem starting from $T1$ assumptions and apply it to show many estimates, including $L^p \times L^q \to L^r$…
Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…
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…
A systematic study of the contributions at infinity for the cohomology of variations of polarized Hodge structures over quasicompact K\"ahler manifolds. Several isomorphisms between different cohomologies given.
We obtain refined generating series formulae for equivariant characteristic classes of external and symmetric products of singular complex quasi-projective varieties. More concretely, we study equivariant versions of Todd, Chern and…
We consider quiver representations respecting a quiver automorphism and show that the dimension vectors of the indecomposables are precisely the positive roots of an associated symmetrisable Kac-Moody Lie algebra. Moreover, every such Lie…
In this paper we describe operads encoding two different kinds of compatibility of algebraic structures. We show that there exist decompositions of these in terms of black and white products and we prove that they are Koszul for a large…
We describe the Chow homology and cohomology of toric variety bundles, with no restrictions on the singularities of the fibre. We present the ordinary and equivariant homologies as modules over the cohomology of the base, identify the…
We discuss a relation between bicomplexes and integrable models, and consider corresponding noncommutative (Moyal) deformations. As an example, a noncommutative version of a Toda field theory is presented.
In this paper we relate the cohomology of $J$-invariant forms to the Dolbeault cohomology of an almost complex manifold. We find necessary and sufficient condition for the inclusion of the former into the latter to be true up to…
We establish direct isomorphisms between different versions of tiling cohomology. The first version is the direct limit of the cohomologies of the approximants in the Anderson-Putnam-G\"ahler complex, the second is the recently introduced…
In this paper we show how wavelets originating from multiresolution analysis of scale N give rise to certain representations of the Cuntz algebras O_N, and conversely how the wavelets can be recovered from these representations. The…
The Lawson homology of a smooth projective variety with a $\C^*$-action is given in terms of that of the fixed point set of this action. We also consider such a decomposition for the Lawson homology of certain singular projective varieties…
Let G be a compact, simple and simply connected Lie group and $\A$ be an equivariant Dixmier-Douady bundle over G. For any fixed level k, we can define a G-C*-algebra $C_{\A^{k+h}}(G)$ as all the continuous sections of the tensor power…
We give a description of the cohomological invariants mod 2 of a Weyl group G in terms of the involution classes of G.