Related papers: Commutator Representations of Covariant Differenti…

A condition is identified which guarantees that the coinvariants of a coaction of a Hopf algebra on an algebra form a subalgebra, even though the coaction may fail to be an algebra homomorphism. A Hilbert Theorem (finite generation of the…

We show that the multiplier algebra of the Fourier algebra on a locally compact group $G$ can be isometrically represented on a direct sum on non-commutative $L^p$ spaces associated to the right von Neumann algebra of $G$. If these spaces…

For transcendental values of $q$ all bicovariant first order differential calculi on the coordinate Hopf algebras of the quantum groups $SL_q(n+1)$ and $Sp_q(2n)$ are classified. It is shown that the irreducible bicovariant first order…

The derivations of a left coideal subalgebra B of a Hopf algebra A which are compatible with the comultiplication of A (that is, the covariant first order differential calculi, as defined by Woronowicz, on a quantum homogeneous space) are…

Let $A$ be a commutative comodule algebra over a commutative bialgebra $H$. The group of invertible relative Hopf modules maps to the Picard group of $A$, and the kernel is described as a quotient group of the group of invertible grouplike…

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…

We briefly report on our result that, if there exists a realization of a Hopf algebra $H$ in a $H$-module algebra $A$, then their cross-product is equal to the product of $A$ itself with a subalgebra isomorphic to $H$ and commuting with…

Any deformation of a Weyl or Clifford algebra A can be realized through a `deforming map', i.e. a formal change of generators in A. This is true in particular if A is covariant under a Lie algebra g and its deformation is induced by some…

Any multiplier Hopf *-algebra} with positive integrals gives rise to a locally compact quantum group (in the sense of Kustermans and Vaes). As a special case of such a situation, we have the compact quantum groups (in the sense of…

We extend ideas developed for the loop representation of quantum gravity to diffeomorphism-invariant gauge theories coupled to fermions. Let P -> Sigma be a principal G-bundle over space and let F be a vector bundle associated to P whose…

Let F be a right Hilbert C*-module over a C*-algebra B, and suppose that F is equipped with a left action, by compact operators, of a second C*-algebra A. Tensor product with F gives a functor from Hilbert C*-modules over A to Hilbert…

Let G be the group of all formal power series starting with x with coefficients in a field k of zero characteristic (with the composition product), and let F[G] be its function algebra. C. Brouder and A. Frabetti introduced a…

Given a Heisenberg algebra A of canonical commutation relations modelled over an infinite-dimensional nuclear space, a Hopf algebra of its quantum deformations is also an algebra of canonical commutation relations whose Fock representation…

A holomorphic discrete series representation $(L_\pi,H_\pi)$ of a connected semi-simple real Lie group $G$ is associated with an irreducible representation $(\pi,V_{\pi})$ of its maximal compact subgroup $K$. The underlying space $H_\pi$…

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 $A$.…

A systematic computational approach for the explicit construction of any quantum Hopf algebra (U_z(g),\Delta_z) starting from the Lie bialgebra (g,\delta) that gives the first-order deformation of the coproduct map \Delta_z is presented.…

We give an analogue of the classical exponential map on Lie groups for Hopf $*$-algebras with differential calculus. The major difference with the classical case is the interpretation of the value of the exponential map, classically an…

In loop quantum gravity in the connection representation, the quantum configuration space $\bar{\mathcal{A}/\mathcal{G}}$, which is a compact space, is much larger than the classical configuration space $\mathcal{A}/% \mathcal{G}$ of…

We propose a nonstandard approach to solving the apparent incompatibility between the coalgebra structure of some inhomogeneous quantum groups and their natural complex conjugation. In this work we sketch the general idea and develop the…

For a $p$-adic field $F$, the space of pro-$p$-Iwahori invariants of a universal supersingular mod $p$ representation $\tau$ of ${\rm GL}_2(F)$ is determined in the works of Breuil, Schein, and Hendel. The representation $\tau$ is…