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.
Gauge theories on deformed spaces.
Generalized Heisenberg algebras, SUSYQM and degeneracies: infinite well and Morse potential.
Generalized hermite polynomials obtained by embeddings of the q-Heisenberg algebra
Several ways to embed q-deformed versions of the Heisenberg algebra into the classical algebra itself are presented. By combination of those embeddings it becomes possible to transform between q-phase-space and q-oscillator realizations of the q-Heisenberg algebra. Using these embeddings the corresponding Schrödinger equation can be expressed by various difference equations. The solutions for two physically relevant cases are found and expressed as Stieltjes Wigert polynomials.
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.
Géométrie de l'espace tangent sur l'hyperboloïde quantique
Hermite -polynomials and -oscillators
Higher dimensional algebra. VII: Groupoidification.
Homotopy theory of Hopf Galois extensions
We introduce the concept of homotopy equivalence for Hopf Galois extensions and make a systematic study of it. As an application we determine all -Galois extensions up to homotopy equivalence in the case when is a Drinfeld-Jimbo quantum group.
Hopf diagrams and quantum invariants.
How to categorify one-half of quantum 𝔤𝔩(1|2)
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).
Integral calculus on (2).
Introduction to noncommutative differential geometry.
Introduction to quantum Lie algebras
Quantum Lie algebras are generalizations of Lie algebras whose structure constants are power series in h. They are derived from the quantized enveloping algebras . The quantum Lie bracket satisfies a generalization of antisymmetry. Representations of quantum Lie algebras are defined in terms of a generalized commutator. The recent general results about quantum Lie algebras are introduced with the help of the explicit example of .
Invariants of three-manifolds, unitary representations of the mapping class group, and numerical calculations.
Jordan-Schwinger representations and factorised Yang-Baxter operators.