Cyclic cohomology of Hopf algebras admitting a modular pair was first defined in [2] and further developed in [3] and [4] in the context of transverse geometry. Their results are followed by several papers computing Hopf cyclic (co)homology of certain Hopf algebras such as [15], [5] and [13]. In a series of papers [1], [10], [11], and [6] the authors developed a theory of cyclic (co)homology wh...

We determine the periodic cyclic homology of the Iwahori-Hecke algebras Hq, for q ∈ C∗ not a “proper root of unity.” (In this paper, by a proper root of unity we shall mean a root of unity other than 1.) Our method is based on a general result on periodic cyclic homology, which states that a “weakly spectrum preserving” morphism of finite type algebras induces an isomorphism in periodic cyclic ...

We construct a stable homotopy refinement of quantum annular homology, link homology theory introduced by Beliakova, Putyra and Wehrli. For each $r\geq 2$ we associate to an $L$ naive $\mathbb{Z}/r\mathbb{Z}$-equivariant spectrum whose cohomology is isomorphic the as modules over $\mathbb{Z}[\mathbb{Z}/r\mathbb{Z}]$. The construction relies on equivariant version Burnside category approach Laws...

We study Hochschild and cyclic homology of finite type algebras using abelian stratifications of their primitive ideal spectrum. Hochschild homology turns out to have a quite complicated behavior, but cyclic homology can be related directly to the singular cohomology of the strata. We also briefly discuss some connections with the representation theory of reductive p–adic groups.

We compute the Hochschild homology and cohomology, and cyclic homology, of almost Calabi-Yau algebras for SU(3) ADE graphs. These almost Calabi-Yau algebras are a higher rank analogue of the pre-projective algebras for Dynkin diagrams, which are SU(2)-related constructions. The Hochschild (co)homology and cyclic homology of A can be regarded as invariants for the braided subfactors associated t...

In this note, we outline the general development of a theory of symmetric homology of algebras, an analog of cyclic homology where the cyclic groups are replaced by symmetric groups. This theory is developed using the framework of crossed simplicial groups and the homological algebra of module-valued functors. The symmetric homology of group algebras is related to stable homotopy theory. Two sp...

The purpose of this paper is to calculate the cyclic homology of rings of integers of global fields. We accomplish this by explicitly computing the homology of the simple complex associated to Tsygan’s double complex. To accomplish this, we first compute the cyclic homology of cyclic algebras, i.e., algebras of the form A = R[t]/(P (t)), where P is a monic polynomial with coefficients in R. Mor...