相关论文: Twisted Homology of Quantum SL(2) - Part II
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of the coordinate algebra of the quantum SL(2) group relative to twisting automorphisms acting by rescaling the standard generators…
The cup and cap product in twisted Hochschild (co)homology is computed for the standard quantum 2-sphere and used to construct a cyclic 2-cocycle that represents the fundamental Hochschild class.
We calculate the twisted Hochschild and cyclic homology (in the sense of Kustermans, Murphy and Tuset) of all Podles quantum spheres relative to arbitary automorphisms. Our calculations are based on a free resolution due to Masuda, Nakagami…
In the present paper we investigate the noncommutative geometry of a class of algebras, called the Hom-associative algebras, whose associativity is twisted by a homomorphism. We define the Hochschild, cyclic, and periodic cyclic homology…
We continue the investigation of twisted homology theories in the context of dimension drop phenomena. This work unifies previous equivariant index calculations in twisted cyclic cohomology. We do this by proving the existence of the…
We generalize quantum Drinfeld Hecke algebras by incorporating a 2-cocycle on the associated finite group. We identify these algebras as specializations of deformations of twisted skew group algebras, giving an explicit connection to…
Many quantum groups and quantum spaces of interest can be obtained by cochain (but not cocycle) twist from their corresponding classical object. This failure of the cocycle condition implies a hidden nonassociativity in the noncommutative…
We show that much of the structure of the 2-sphere as a complex curve survives the q-deformation and has natural generalizations to the quantum 2-sphere - which, with additional structures, we identify with the quantum projective line.…
We study the relationship between trivial cocycles on the Torelli group and invariants of oriented integral homology 3-spheres. We give ncecessary and sufficient conditions for a function defined on the union of the Torelli groups to be an…
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…
We study the twisted Hochschild homology of quantum full flag manifolds, with the twist being the modular automorphism of the Haar state. We show that non-trivial 2-cycles can be constructed from appropriate invariant projections. The main…
We calculate the Hochschild dimension of quantum hyperplanes using the twisted Hochschild homology.
For two covariant differential *-calculi, the twisted cyclic cocycle associated with the volume form is represented in terms of commutators [F,\rho(x)] for some self-adjoint operator F and some *-representation $\rho$ of the underlying…
Quantum symmetric algebras (or noncommutative polynomial rings) arise in many places in mathematics. In this article we find the multiplicative structure of their Hochschild cohomology when the coefficients are in an arbitrary bimodule…
The purpose of the paper is twofold: First, known results of the noncommutative spin geometry of the standard Podles sphere are extended by discussing Poincare duality and orientability. In the discussion of orientability, Hochschild…
We calculate the additive and multiplicative structure (together with the grading) of the Hochschild homology and cohomology and the cyclic homology of preprojective algebras of types T. We also compute the calculus structure which is…
We give a construction of cyclic cocycles on convolution algebras twisted by gerbes over discrete translation groupoids. For proper \'etale groupoids, Tu and Xu provide a map between the periodic cyclic cohomology of a gerbe-twisted…
The Hochschild homology of the ring $k[x_1,x_2,\ldots,x_d]/(x_1,x_2,\ldots,x_d)^2$ has been known and calculated several ways. This paper uses those calculations to calculate cyclic, negative cyclic, and periodic cyclic homology of…
Adapting the idea of twisted tensor products to the category of finitely generated algebras, we define on its opposite, the category QLS of quantum linear spaces, a family of objects hom(B,A)^{op}, one for each pair A^{op},B^{op} there,…
We calculate the third homology of $\mathrm{SL}_2(\mathbb{Q})$ with half-integral coefficients. Corresponding to each prime $p$ there is an operator on this group with square the identity. The kernel of the (split surjective) homomorphism…