Hochschild and Cyclic Homology of Quantum Kummer Spaces
We study the quotient space obtained by the flip action on the quantum n-tori. The Hochschild, cyclic and periodic cyclic homology are calculated.
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arXiv subjects
Safdar Quddus
Publications and source records attributed to Safdar Quddus.
Non-commutative Poisson Structures on quantum torus orbifolds
We study the Hochschild cohomology and the Gerstenhaber algebra structure on the algebraic non-commutative torus/quantum torus orbifolds resulting by the action of finite subgroups of $SL_2(\mathbb Z)$. We also examine the Poisson structures and compute the Poisson cohomology.
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Equivariant Cartan Homotopy Formulae for $DG$-Algebra
We study the Equivariant Cartan Homotopy Formula for the $DG$-algebra obtained by a finite group action.
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Invariants of the $\mathbb Z_2$ orbifolds of the Podleś' two spheres
There are two $\mathbb Z_2$ orbifolds of the Podleś quantum two-sphere, one being the quantum two-disc $D_q$ and other the quantum two-dimensional real projective space $\mathbb RP^2_q$ . In this article we calculate the Hochschild and cyclic homology and cohomology groups of these orbifolds and also the corresponding Chern-Connes indices.
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Cohomology of $\mathcal A_θ^{alg} \rtimes \mathbb Z_2$ and its Chern-Connes pairing
We calculate the Hochschild and cyclic cohomology of the $\mathbb Z_2$ toroidal orbifold $\mathcal A_θ^{alg} \rtimes \mathbb Z_2$. We also calculate the Chern-Connes pairing of the even cyclic cohomology group with the known elements of $K_0(\mathcal A_θ^{alg} \rtimes \mathbb Z_2)$.
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Cyclic Cohomology and Chern Connes pairing of some crossed product algebras
We compute the cyclic and Hochschild cohomology groups for the algebras $\mathcal A_θ^{alg} \rtimes \mathbb Z_3, \mathcal A_θ^{alg} \rtimes \mathbb Z_4$ and $\mathcal A_θ^{alg} \rtimes \mathbb Z_6$. We also compute the partial Chern-Connes index table for each of these algebras.
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Hochschild and cyclic homology of the crossed product of algebraic irrational rotational algebra by finite subgraoups of $SL(2,\mathbb Z)$
Let $Γ\subset SL(2, \mathbb Z)$ be a finite subgroup acting on the irrational rotational algebra $\mathcal A_θ$ via the restriction of the canonical action of $SL(2,\mathbb Z)$. Consider the crossed product algebra $\mathcal A_θ^{alg} \rtimes Γ$ obtained by the restriction of the $Γ$ action on the algberaic irrational rotational algebra. In this paper we prove many results on the homology group of the crossed product algebra $\mathcal A_θ^{alg} \rtimes Γ$. We also analyse the case of the smooth crossed product algebra, $\mathcal A_θ\rtimes Γ$ and calculate some of its homology groups.
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