The Fourier transform on quantum Euclidean space.
The garden of quantum spheres
A list of known quantum spheres of dimension one, two and three is presented.
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 rational qKZ equation and shifted non-symmetric Jack polynomials.
The spectrum of coupled random matrices.
The structure of corings with a grouplike element
Characteristic properties of corings with a grouplike element are analysed. Associated differential graded rings are studied. A correspondence between categories of comodules and flat connections is established. A generalisation of the Cuntz-Quillen theorem relating existence of connections in a module to projectivity of this module is proven.
The Yang-Baxter and pentagon equation
Traces dans les catégories monoïdales, dualité et catégories monoïdales fibrées
Translation-invariant noncommutative renormalization.
Triangular Lie bialgebras and matched pairs for Lie algebras of real vector fields on .
Twisted quantum doubles.
Twisted spectral triples and covariant differential calculi
Connes and Moscovici recently studied "twisted" spectral triples (A,H,D) in which the commutators [D,a] are replaced by D∘a - σ(a)∘D, where σ is a second representation of A on H. The aim of this note is to point out that this yields representations of arbitrary covariant differential calculi over Hopf algebras in the sense of Woronowicz. For compact quantum groups, H can be completed to a Hilbert space and the calculus is given by bounded operators. At the end, we discuss an explicit example of...
Two classical results in the quantum mixed case.
Universal Bethe ansatz and scalar products of Bethe vectors.
Universal -differential calculus and -analog of homological algebra.
Universal Verma modules and the Misra-Miwa Fock space.
Weak c*-Hopf algebras: the coassociative symmetry of non-integral dimensions
By allowing the coproduct to be non-unital and weakening the counit and antipode axioms of a C*-Hopf algebra too, we obtain a selfdual set of axioms describing a coassociative quantum group, that we call a weak C*-Hopf algebra, which is sufficiently general to describe the symmetries of essentially arbitrary fusion rules. It is the same structure that can be obtained by replacing the multiplicative unitary of Baaj and Skandalis with a partial isometry. The algebraic properties, the existence of...
-Minkowski spacetimes and DSR algebras: fresh look and old problems.
Деформированные осцилляторы и их приложения
Инвариант триангулированных зацеплений из квантового дилогарифма