The cyclic homology of
The dynamical quantum group.
The elliptic dynamical quantum group as an -Hopf algebroid.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
The geometric reductivity of the quantum group
We introduce the concept of geometrically reductive quantum group which is a generalization of the Mumford definition of geometrically reductive algebraic group. We prove that if G is a geometrically reductive quantum group and acts rationally on a commutative and finitely generated algebra A, then the algebra of invariants is finitely generated. We also prove that in characteristic 0 a quantum group G is geometrically reductive if and only if every rational G-module is semisimple, and that in...
The Harish-Chandra homomorphism for a quantized classical hermitian symmetric pair
Let a noncompact symmetric space with Iwasawa decomposition . The Harish-Chandra homomorphism is an explicit homomorphism between the algebra of invariant differential operators on and the algebra of polynomials on that are invariant under the Weyl group action of the pair . The main result of this paper is a generalization to the quantum setting of the Harish-Chandra homomorphism in the case of being an hermitian (classical) symmetric space
The Khovanov-Lauda 2-category and categorifications of a level two quantum representation.
The Kontsevich integral and quantized Lie superalgebras.
The multisegment duality and the preprojective algebras of type .
The quantum double of a (locally) compact group.
The quantum duality principle
The “quantum duality principle” states that the quantization of a Lie bialgebra – via a quantum universal enveloping algebra (in short, QUEA) – also provides a quantization of the dual Lie bialgebra (through its associated formal Poisson group) – via a quantum formal series Hopf algebra (QFSHA) — and, conversely, a QFSHA associated to a Lie bialgebra (via its associated formal Poisson group) yields a QUEA for the dual Lie bialgebra as well; more in detail, there exist functors and , inverse to...
The relationship between Zhedanov's algebra and the double affine Hecke algebra in the rank one case.
The Robinson-Schensted correspondence, crystal bases, and the quantum straightening at .
The Yang-Baxter and pentagon equation
Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées
Triangular Lie bialgebras and matched pairs for Lie algebras of real vector fields on .
Twisted quantum doubles.
Twisted vertex representations of quantum affine algebras.
Two applications of elementary knot theory to Lie algebras and Vassiliev invariants.
Two classical results in the quantum mixed case.