Related papers: Quantum Real Projective Space, Disc and Sphere

We give a general methodology for constructing split exact sequences of amplified graph C*-algebras with sinks. This in turn allows us to construct explicit KK-equivalences with $\mathbb{C}^N$ for a large class of C*-algebras, including the…

The universal C*-algebra generated by n projections has been described. As an immediate corollary one obtains structure theorem for a pair of projections and the solution to an associated index problem. This puts the study of a pair of…

We show that the endomorphism ring of any nonzero finitely generated projective module over the Leavitt path algebra $L_K(E)$ of an arbitrary graph $E$ with coefficients in a field $K$ is isomorphic to a Steinberg algebra. This yields in…

Using the corepresentation of the quantum supergroup OSp_q(1/2) a general method for constructing noncommutative spaces covariant under its coaction is developed. In particular, a one-parameter family of covariant algebras, which may be…

We introduce two new formulations for the notion of "quantum metric on noncommutative space". For a compact noncommutative space associated to a unital C*-algebra, our quantum metrics are elements of the spatial tensor product of the…

The Noncommutative Index Theorem is used to prove that the Chern character of quantum Hopf line bundles over the standard Podles quantum sphere equals the winding number of the representations defining these bundles. This result gives an…

We develop the noncommutative geometry (bundles, connections etc.) associated to algebras that factorise into two subalgebras. An example is the factorisation of matrices $M_2(\C)=\C\Z_2\cdot\C\Z_2$. We also further extend the coalgebra…

For a completely Hausdorff quasi-topological group $G$, we construct a universal pro-$C^*$-algebra $C(E^+G)$ as the non-commutative geometer's analogue of the total space $EG$ of the classifying principal $G$-bundle $EG\to BG$. The…

We construct an irreducible embedded projective plane in $S^4$. This gives a counterexample to the Kinoshita conjecture and answers Problem 4.37 of the K3 problem list. Moreover, we answer both Questions (i) and (ii) of Problem 4.37: (i)…

We study the quantum sphere $C_q[S^2]$ as a quantum Riemannian manifold in the quantum frame bundle approach. We exhibit its 2-dimensional cotangent bundle as a direct sum $\Omega^{0,1}\oplus\Omega^{1,0}$ in a double complex. We find the…

Let k be a perfect field and let K/k be a finite extension of fields. An arithmetic noncommutative projective line is a noncommutative space equal to the projectivization of the noncommutative symmetric algebra of a k-central two -sided…

We show that every smooth toric variety (and many other algebraic spaces as well) can be realized as a moduli space for smooth, projective, polarized varieties. Some of these are not quasi--projective. This contradicts a recent paper…

We show how the quantum trace map of Bonahon and Wong can be constructed in a natural way using the skein algebra of Muller, which is an extension of the Kauffman bracket skein algebra of surfaces. We also show that the quantum…

We show that a $KK$-equivalence between two unital $C^*$-algebras produces a correspondence between their DG categories of finitely generated projective modules which is a $\mathbf{K}_*$-equivalence, where $\mathbf{K}_*$ is Waldhausen's…

Suppose q is a complex number of modulus one and different from 1,-1. Let O(R^2_q) be the *-algebra with two hermitean generators x and y satisfying the relation xy=qyx. Using operator representations of the *-algebra O(R^2_q) on Hilbert…

We define a natural quantum analogue for the ${\cal Z}$ algebra, and which we refer to as the ${\cal Z}_q$ algebra, by modding out the Heisenberg algebra from the quantum affine algebra $U_q(\hat{sl(2)})$ with level $k$. We discuss the…

We introduce and analyse a new type of quantum 2-spheres. Then we apply index theory for noncommutative line bundles over these spheres to conclude that quantum lens spaces are non-crossed-product examples of principal extensions of…

We study irreducible *-representations of a certain quantization of the algebra of polynomial functions on a generalized flag manifold regarded as a real manifold. All irreducible *-representations are classified for a subclass of flag…

We present the complete set of $N=1$, $D=4$ quantum algebras associated to massive superparticles. We obtain the explicit solution of these algebras realized in terms of unconstrained operators acting on the Hilbert space of superfields.…

Consider the compact quantum group $U_q(2)$, where $q$ is a non-zero complex deformation parameter such that $|q|\neq 1$. Let $C(U_q(2))$ denote the underlying $C^*$-algebra of the compact quantum group $U_q(2)$. We prove that if $q$ is a…