Related papers: Remarks on the Quantum Bohr Compactification

We introduce the notion of Hopf algebroids, in which neither the total algebras nor the base algebras are required to be commutative. We give a class of Hopf algebroids associated to module algebras of the Drinfeld doubles of Hopf algebras…

The renormalization of quantum field theory twists the antipode of a noncocommutative Hopf algebra of rooted trees, decorated by an infinite set of primitive divergences. The Hopf algebra of undecorated rooted trees, ${\cal H}_R$, generated…

Rational Hopf algebras (certain quasitriangular weak quasi-Hopf $^*$-algebras) are expected to describe the quantum symmetry of rational field theories. In this paper methods are developped which allow for a classification of all rational…

Given a finite group $G$, we introduce "encoding pairs," which are a pair of $G$-modules $M$ and $M'$ equipped with a shifted natural isomorphism between the cohomological functors $H^\bullet(G,\mathrm{Hom}_\mathbb Z(M,-))$ and…

The generalization of multiplicative unitary notion from compact quantum groups to compact quantum semigroups is considered. We show why the same construction doesn't work in this case by giving examples of C*-algebras with non-trivial…

We report some observations concerning two well-known approaches to construction of quantum groups. Thus, starting from a bialgebra of inhomogeneous type and imposing quadratic, cubic or quartic commutation relations on a subset of its…

We expose a K-theoretic approach to study group C*-algebras and C*-algebraic compact quantum groups: 1. The conception of multidimensional geometric quantization and the index of group C*-algebras; 2. the entire homology of noncommutative…

Let A be a finite dimensional Hopf algebra and (H, R) a quasitriangular bialgebra. Denote by H^*_R a certain deformation of the multiplication of H^* via R. We prove that H^*_R is a quantum commutative left H\otimes H^{op cop}-module…

We introduce the notions of Hopf quasigroup and Hopf coquasigroup $H$ generalising the classical notion of an inverse property quasigroup $G$ expressed respectively as a quasigroup algebra $k G$ and an algebraic quasigroup $k[G]$. We prove…

For a Banach algebra $A$ with a bounded approximate identity, we investigate the $A$-module homomorphisms of certain introverted subspaces of $A^*$, and show that all $A$-module homomorphisms of $A^*$ are normal if and only if $A$ is an…

Let $G$ be a locally compact group, and consider the weakly-almost periodic functionals on $M(G)$, the measure algebra of $G$, denoted by $\wap(M(G))$. This is a C$^*$-subalgebra of the commutative C$^*$-algebra $M(G)^*$, and so has…

We prove two versions of Bochner's theorem for locally compact quantum groups. First, every completely positive definite "function" on a locally compact quantum group $\G$ arises as a transform of a positive functional on the universal…

A notion of L^2-homology for compact quantum groups is introduced, generalizing the classical notion for countable, discrete groups. If the compact quantum group in question has tracial Haar state, it is possible to define its L^2-Betti…

Let k be a non archimedean field. If X is a k-algebraic variety and U a locally closed semi-algebraic subset of X^{an} -- the Berkovich space associated to X -- we show that for l \neq char(\tilde{k}), the cohomology groups H^i_c (\bar{U},…

Suppose $\mathcal{G}$ is a second-countable locally compact Hausdorff \'{e}tale groupoid, $G$ is a discrete group containing a unital subsemigroup $P$, and $c:\mathcal{G}\rightarrow G$ is a continuous cocycle. We derive conditions on the…

We show that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then one can split their cross-product into the tensor product algebra of $A$ itself with a subalgebra isomorphic to $H$ and commuting with $A$.…

We present a general theory of braided quantum groups in the C*-algebraic framework using the language of multiplicative unitaries. Starting with a manageable multiplicative unitary in the representation category of the quantum codouble of…

We introduce an extended setting to study Hecke pairs $(G,H)$ which admit a regular representation on $L^2(H\backslash G)$, and consequently a $C^*$-algebra. As the result, many pairs of locally compact groups which had been studied in…

We show that every partial representation of a connected Hopf algebra is global. Some interesting classes of partial representations of smash product Hopf algebras are studied, and a description of the partial "Hopf" algebra if the first…

To characterize categorical constraints - associativity, commutativity and monoidality - in the context of quasimonoidal categories, from a cohomological point of view, we define the notion of a parity (quasi)complex. Applied to groups…