Related papers: Spectral Triples for Hensel-Steinitz Algebras
The purpose of this paper is to present a simple and explicit construction of the Bokstedt-Hsiang-Madsen cyclotomic trace relating algebraic K-theory and topological cyclic homology. Our construction also incorporates Goodwillie's idea of a…
The aim of the present work is to show how, using the differential calculus associated to Dirichlet forms, it is possible to construct Fredholm modules on post critically finite fractals by regular harmonic structures. The modules are…
We advance the understanding of K-theory of quadratic forms by computing the slices of the motivic spectra representing hermitian K-groups and Witt-groups. By an explicit computation of the slice spectral sequence for higher Witt-theory, we…
We introduce a new class of $\mathfrak{sl}_2$-triples in a complex simple Lie algebra $\mathfrak{g}$, which we call magical. Such an $\mathfrak{sl}_2$-triple canonically defines a real form and various decompositions of $\mathfrak{g}$.…
We use homological ideals in triangulated categories to get a sufficient criterion for a pair of subcategories in a triangulated category to be complementary. We apply this criterion to construct the Baum-Connes assembly map for locally…
A triple of spectra (r^A, r^B, r^{AB}) is said to be admissible if there is a density operator rho^{AB} with (Spec rho^A, Spec rho^B, Spec rho^{AB})=(r^A, r^B, r^{AB}). How can we characterise such triples? It turns out that the admissible…
The goal of this paper is to compute the supports of simple modules in the categories $\mathcal{O}$ for the rational Cherednik algebras associated to groups $G(\ell,1,n)$. For this we compute some combinatorial maps on the set of simples:…
We construct chain maps between the bar and Koszul resolutions for a quantum symmetric algebra (skew polynomial ring). This construction uses a recursive technique involving explicit formulae for contracting homotopies. We use these chain…
This is the second paper in a series of three papers aiming to study cohomology of group theoretic Dehn fillings. In the present paper, we derive a spectral sequence for Cohen-Lyndon triples which can be thought of as a refined version of…
We investigate the representations and the structure of Hecke algebras associated to certain finite complex reflection groups. We first describe computational methods for the construction of irreducible representations of these algebras,…
The notion of a K\"ahler structure for a differential calculus was recently introduced by the second author as a framework in which to study the noncommutative geometry of the quantum flag manifolds. It was subsequently shown that any…
We consider the concept of fractons, i.e. particles or quasiparticles which obey specific fractal distribution function and for each universal class h of particles we obtain a fractal-deformed Heisenberg algebra. This one takes into account…
Let $A$ be a dense Fr\'echet subalgebra of the $C^\star$-algebra of compact operators $\cal K$ on a seprable Hilbert space. Assume that $A$ is spectral invariant in $\cal K$. We show that every algebraically cyclic subrepresentation of a…
We establish an algebra-isomorphism between the complexified Grothendieck ring F of certain bimodule categories over a modular tensor category and the endomorphism algebra of appropriate morphism spaces of those bimodule categories. This…
In order to study the Hochschild cohomology of triangular algebras $\mathcal T$, we construct a spectral sequence, whose terms are parametrized by the length of the trajectories of the quiver associated with $\mathcal T$, and which…
We discuss notions of almost complex, complex and K\"{a}hler structures in the realm of non-commutative geometry and investigate them for a class of finite dimensional spectral triples on the three-point space. We classify all the almost…
We develop a version of controlled algebra for simplicial rings. This generalizes the methods which lead to successful proofs of the algebraic K- theory isomorphism conjecture (Farrell-Jones Conjecture) for a large class of groups. This is…
In the classical operator theory, there are several versions of spectra, related to special classes of operators (Fredholm, semi-Fredholm, upper/lower semi-Fredholm,etc.). We generalize these notions for adjointable operators on Hilbert…
Let $a$ and $b$ be two coprime positive integers and $k$ an arbitrary field. We determine the ring structure of the Hochschild cohomology of the numerical semigroup algebras $k[s^{a},s^{b}]$ of embedding dimension two (thus also complete…
We give a geometrical construction of Connes spectral triples or noncommutative Dirac operators $D$ starting with a bimodule connection on the proposed spinor bundle. The theory is applied to the example of $M_2(\Bbb C)$, and also applies…