Dynamical matrices of elliptic quantum groups and connection matrices for the -KZ equations.
Epsilon systems on geometric crystals of type .
Équations de Knizhnik-Zamolodchikov et théorie des représentations
Equivariant Morita equivalences between Podleś spheres
We show that the family of Podleś spheres is complete under equivariant Morita equivalence (with respect to the action of quantum SU(2)), and determine the associated orbits. We also give explicit formulas for the actions which are equivariantly Morita equivalent with the quantum projective plane. In both cases, the computations are made by examining the localized spectral decomposition of a generalized Casimir element.
Exact Lie Bialgebroids and Poisson Groupoids.
Examples of liftings of Nichols algebras over racks.
Examples of tensor categories.
Exponentiations over the quantum algebra
We define and compare, by model-theoretical methods, some exponentiations over the quantum algebra . We discuss two cases, according to whether the parameter is a root of unity. We show that the universal enveloping algebra of embeds in a non-principal ultraproduct of , where varies over the primitive roots of unity.
Filtrations and tilting modules
First order calculi with values in right-universal bimodules
The purpose of this note is to show how calculi on unital associative algebra with universal right bimodule generalize previously studied constructions by Pusz and Woronowicz [1989] and by Wess and Zumino [1990] and that in this language results are in a natural context, are easier to describe and handle. As a by-product we obtain intrinsic, coordinate-free and basis-independent generalization of the first order noncommutative differential calculi with partial derivatives.
Free dynamical quantum groups and the dynamical quantum group
We introduce dynamical analogues of the free orthogonal and free unitary quantum groups, which are no longer Hopf algebras but Hopf algebroids or quantum groupoids. These objects are constructed on the purely algebraic level and on the level of universal C*-algebras. As an example, we recover the dynamical studied by Koelink and Rosengren, and construct a refinement that includes several interesting limit cases.
Free field approach to solutions of the quantum Knizhnik-Zamolodchikov equations.
From double Lie groups to quantum groups
It is shown, using geometric methods, that there is a C*-algebraic quantum group related to any double Lie group (also known as a matched pair of Lie groups or a bicrossproduct Lie group). An algebra underlying this quantum group is the algebra of a differential groupoid naturally associated with the double Lie group.
Fundamental representations of Yangians and singularities of R-matrices.
Generalized Hurwitz maps of the type S × V → W, anti-involutions, and quantum braided Clifford algebras
The notion of a -triple is studied in connection with a geometrical approach to the generalized Hurwitz problem for quadratic or bilinear forms. Some properties are obtained, generalizing those derived earlier by the present authors for the Hurwitz maps S × V → V. In particular, the dependence of each scalar product involved on the symmetry or antisymmetry is discussed as well as the configurations depending on various choices of the metric tensors of scalar products of the basis elements. Then...
Generalized radical rings, unknotted biquandles, and quantum groups
Generalized radical rings (braces) were introduced for the study of set-theoretical solutions of the quantum Yang-Baxter equation. We discuss their relationship to groups of I-type, virtual knot theory, and quantum groups.
Generating series for nested Bethe vectors.
Generators and relations for Schur algebras.
Generic extensions of nilpotent k[T]-modules, monoids of partitions and constant terms of Hall polynomials
We prove that the monoid of generic extensions of finite-dimensional nilpotent k[T]-modules is isomorphic to the monoid of partitions (with addition of partitions). This gives us a simple method for computing generic extensions, by addition of partitions. Moreover we give a combinatorial algorithm that calculates the constant terms of classical Hall polynomials.
Generic modules over the quantum group Ut (sl(2)) at t a root of unit.