Related papers: Quantum Real Projective Space, Disc and Sphere
We discuss generalizations of the notion of i) the group of unitary elements of a (real or complex) finite dimensional C*-algebra, ii) gauge transformations and iii) (real) automorphisms, in the framework of compact quantum group theory and…
We generalize to quantum weighted projective spaces in any dimension previous results of us on K-theory and K-homology of quantum projective spaces `tout court'. For a class of such spaces, we explicitly construct families of Fredholm…
We show that the quantum disk, i.e. the quantum space corresponding to the Toeplitz C*-algebra does not admit any compact quantum group structure. We prove that if such a structure existed the resulting compact quantum group would…
We study irreducible representations of a class of quantum spheres, quotients of quantum symplectic spheres.
In this paper, we study a generalization of the notion of AS-regularity for connected $\mathbb{Z}$-algebras. Our main result is a characterization of those categories equivalent to noncommutative projective schemes associated to right…
In this paper, we study the structure of the quantum cohomology ring of a projective hypersurface with non-positive 1st Chern class. We prove a theorem which suggests that the mirror transformation of the quantum cohomology of a projective…
We generalize a theorem of Kapranov by showing that the Hall algebra of the category of coherent sheaves on a weighted projective line (over a finite field) provides a realization of the (quantized) enveloping algebra of a certain nilpotent…
We calculate K-theory of a crossed product $C^*$-algebra of the noncommutative torus with real multiplication by elliptic curve $\mathscr{E}(K)$ over a number field $K$. This result is used to evaluate the rank and the Shafarevich-Tate…
We study the quantization of spaces whose K-theory in the classical limit is the ring of dual numbers $\mathbb{Z}[t]/(t^2)$. For a compact Hausdorff space we recall necessary and sufficient conditions for this to hold. For a compact quantum…
There are theories of coverings of $C^*$-algebras which can be included into a following list: coverings of commutative $C^*$-algebras, coverings of $C^*$-algebras of groupoids and foliations, coverings of noncommutative tori, the double…
Much of the work in loop quantum gravity and quantum geometry rests on a mathematically rigorous integration theory on spaces of distributional connections. Most notably, a diffeomorphism invariant representation of the algebra of basic…
We discuss spectral properties of the equatorial Podles sphere. As a preparation we also study the `degenerate' (i.e. $q=0$) case (related to the quantum disk). We consider two different spectral triples: one related to the Fock…
We introduce the notion of pure Q-solvable algebra. The quantum matrices, quantum Weyl algebra, U_q(n) are the examples. It is proved that the skew field of fractions of pure Q-solvable algebra is isomorphic to the skew field of twisted…
In this paper, we study in the context of quantum vertex algebras a certain Clifford-like algebra introduced by Jing and Nie. We establish bases of PBW type and classify its $\mathbb N$-graded irreducible modules by using a notion of Verma…
This is a survey paper about representation theory and noncommutative geometry of reductive p-adic groups G. The main focus points are: 1. The structure of the Hecke algebra H(G), the Harish-Chandra-Schwartz algebra S(G) and the reduced…
In this letter we derive a deformed Dirac equation invariant under the k-Poincare` quantum algebra. A peculiar feature is that the square of the k-Dirac operator is related to the second Casimir (the k-deformed squared Pauli-Lubanski…
In this note we analyze the C*-algebra associated with a branched covering both as a groupoid C*-algebra and as a Cuntz-Pimsner algebra. We determine conditions when the algebra is simple and purely infinite. We indicate how to compute the…
We revisit the notion of quantum Lie algebra of symmetries of a noncommutative spacetime, its elements are shown to be the generators of infinitesimal transformations and are naturally identified with physical observables. Wave equations on…
We give a non-commutative Positivstellensatz for CP^n: The (commutative) *-algebra of polynomials on the real algebraic set CP^n with the pointwise product can be realized by phase space reduction as the U(1)-invariant polynomials on…
We work on the classification of isomorphism classes of finitely generated projective modules over the C*-algebras $C\left( \mathbb{P}^{n}\left( \mathcal{T}\right) \right) $ and $C\left( \mathbb{S}_{H}^{2n+1}\right) $ of the quantum complex…