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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.
A generalized Steinberg section and branching rules for quantum groups at roots of 1
generalized Steinberg section branching rules quantum groups
2011/8/23
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...
Manin triples and differential operators on quantum groups
Manin triples differential operators quantum groups
2011/1/18
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...
On Square Roots of the Haar State on Compact Quantum Groups
Compact quantum group Haar state normal subgroup
2011/1/20
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 ...
Path subcoalgebras, finiteness properties and quantum groups
incidence coalgebra path coalgebra co-Frobenius coalgebra quasi-co-Frobenius coalgebra
2011/2/24
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...