Recently the operator algebra, including the twisted affine primary fields, and a set of twisted KZ equations were given for the WZW permutation orbifolds. In the first part of this paper we extend this operator algebra to include the so-called orbifold Virasoro algebra of each WZW permutation orbifold. These algebras generalize the orbifold Virasoro algebras (twisted Virasoro operators) found ...

An extension of bornological algebras with a bounded linear section gives rise to a six term exact sequence of the associated periodic and entire cyclic cohomology groups. 1. Introduction A convex vector bornology on a vector space is a collection of subsets satisfying some conditions 8]. A typical example is the collection of bounded subsets of a locally convex vector space. A bornological alg...

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn o C`, the wreath product of the symmetric group and the cyclic group of order `, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size `. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...

In this paper, we further explore the conceptual approach to cyclic cohomology with coefficients initiated in [HKS]. In particular we give a derived version of the definition with better invariance properties. We show that the new definition agrees with the old under certain conditions and we prove, for the new definition, both its Morita invariance and its 2-Morita invariance, under suitable i...

We show that the spherical subalgebra Uk,c of the rational Cherednik algebra associated to Sn ≀ Cl, the wreath product of the symmetric group and the cyclic group of order l, is isomorphic to a quotient of the ring of invariant differential operators on a space of representations of the cyclic quiver of size l. This confirms a version of [EG, Conjecture 11.22] in the case of cyclic groups. The ...

Let X be a manifold on which a discrete (pseudo)group of diffeomorphisms Γ acts, and let E be a Γ-equivariant vector bundle on X. We give a construction of cyclic cocycles on the cross product algebra C∞ 0 (X)o Γ representing the equivariant characteristic classes of E. Our formulas can be viewed as a higher-dimensional analogue of Connes’ Godbillon-Vey cyclic cocycle. An essential tool for our...

In this paper we deal with Calabi-Yau structures associated (differential graded versions of) deformed multiplicative preprojective algebras, of which provide concrete algebraic descriptions. Along the way, prove a general result that states existence and uniqueness negative cyclic lifts for non-degenerate relative Hochschild classes.

Let K/F and K/L be two cyclic Galois field extensions and D = (K/F, σ, c) a cyclic algebra. Given an invertible element d ∈ D, we present three families of unital nonassociative algebras over L ∩ F defined on the direct sum of n copies of D. Two of these families appear either explicitly or implicitly in the designs of fast-decodable space-time block codes in papers by Srinath, Rajan, Markin, O...

We give an introductory survey to the use of Hopf algebras in several problems of noncommutative geometry. The main example, the Hopf algebra of rooted trees, is a graded, connected Hopf algebra arising from a universal construction. We show its relation to the algebra of transverse differential operators introduced by Connes and Moscovici in order to compute a local index formula in cyclic coh...

We study in detail the spectrum of the bosonic oscillator Hamiltonian associated with the C3-extended oscillator algebra A α0α1 , where C3 denotes a cyclic group of order three, and classify the various types of spectra in terms of the algebra parameters α0, α1. In such a classification, we identify those spectra having an infinite number of periodically spaced levels, similar to those of cycli...