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Let S be a monoidal category with equalizers that are preserved by the tensor product. The notion of categories internal to S is defined, generalizing the notions of monoid and comonoid in S, and ex...
The classical identities between the q-binomial coefficients and factorials can be gener- alized to a context where numbers are replaced by braids. More precisely, for every pair i, n of natural num...
In this paper we realize some powers of Dedekind \eta-function as the trace of an operator on quantum coordinate algebras.
Abstract: We show that any completely positive multiplier of the convolution algebra of the dual of an operator algebraic quantum group $\G$ (either a locally compact quantum group, or a quantum group...
Abstract: Given a locally compact quantum group $\G$, we study the question of when completely bounded homomorphisms $\pi:L^1(\mathbb G)\rightarrow\mathcal B(H)$ are similar to *-homomorphisms. By ana...
Abstract: In this paper we construct a generalization of the classical Steinberg section for the quotient map of a semisimple group with respect to the conjugation action. We then give various applica...
Let (a,m, l) be a Manin triple, and let M, L be algebraic groups with Lie algebras m, l respectively. We point out that the product M×L carries a natural structure of Poisson manifold,whose Poisson te...
Transmission matrices for two types of integrable defect are calculated explicitly, first by solving directly the nonlinear transmission Yang-Baxter equations.
The paper is concerned with the extension of the classical study of probability measures on a compact group which are square roots of the Haar measure, due to Diaconis and Shahshahani, to the context ...
We study subcoalgebras of path coalgebras that are spanned by paths (called path subcoalgebras) and subcoalgebras of incidence coalgebras, and propose a unifying approach for these classes.
We introduce some equivalent notions of homomorphisms between quantum groups that behave well with respect to duality of quantum groups. Our equivalent definitions are based on bicharacters, coactions...
In this paper, we quantize universal gauge groups such as SU(\infty), in the sigma-C*-algebra setting. More precisely, we propose a concise definition of sigma-C*-quantum groups and explain the conce...
We introduce the notion of a relative spherical category. We prove that such a category gives rise to the generalized Kashaev and Turaev-Viro-type 3-manifold invariants de ned in [12] and [17], respe...
We give a construction of a Dirac operator on a quantum group based on any simple Lie algebra of classical type. The Dirac operator is an element in the vector space clq(g) U q(g), where the first t...

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