Quantum integrable 1D anyonic models: construction through braided Yang-Baxter equation.
Quantum integrable model of an arrangement of hyperplanes.
Quantum integrable systems
Quantum invariants of links and 3-valent graphs in 3-manifolds
Quantum isometries and group dual subgroups
We study the discrete groups whose duals embed into a given compact quantum group, . In the matrix case the embedding condition is equivalent to having a quotient map , where is a certain family of groups associated to . We develop here a number of techniques for computing , partly inspired from Bichon’s classification of group dual subgroups . These results are motivated by Goswami’s notion of quantum isometry group, because a compact connected Riemannian manifold cannot have non-abelian...
Quantum isometry group for spectral triples with real structure.
Quantum link invariant from the Lie superalgebra .
Quantum Racah coefficients and subrepresentation semirings.
Quantum sections and Gauge algebras.
Using quantum sections of filtered rings and the associated Rees rings one can lift the scheme structure on Proj of the associated graded ring to the Proj of the Rees ring. The algebras of interest here are positively filtered rings having a non-commutative regular quadratic algebra for the associated graded ring; these are the so-called gauge algebras obtaining their name from special examples appearing in E. Witten's gauge theories. The paper surveys basic definitions and properties but concentrates...
Quantum spaces: notes and comments on a lecture by S. L. Woronowicz
Quantum stochastic convolution cocycles -algebraic and C*-algebraic
We summarise recent results concerning quantum stochastic convolution cocycles in two contexts-purely algebraic and C*-algebraic. In each case the class of cocycles arising as the solution of a quantum stochastic differential equation is characterised and the form taken by the stochastic generator of a *-homomorphic cocycle is described. Throughout the paper a common viewpoint on the algebraic and C*-algebraic situations is emphasised; the final section treats the unifying example of convolution...
Quantum Weyl group and some [of] its applications
Quantum-classical interactions and galois type extensions
An algebraic model for the relation between a certain classical particle system and the quantum environment is proposed. The quantum environment is described by the category of possible quantum states. The initial particle system is represented by an associative algebra in the category of states. The key new observation is that particle interactions with the quantum environment can be described in terms of Hopf-Galois theory. This opens up a possibility to use quantum groups in our model of particle...
Quasi-bigèbres jacobiennes
Quasi-commutative polynomial algebras and the power property of 2 × 2 quantum matrices
Quasigraded Lie algebras and modified Toda field equations.
Quasi-linear algebras and integrability (the Heisenberg picture).
Quasi-particle fermionic formulas for (k, 3)-admissible configurations
We construct new monomial quasi-particle bases of Feigin-Stoyanovsky type subspaces for the affine Lie algebra sl(3;ℂ)∧ from which the known fermionic-type formulas for (k, 3)-admissible configurations follow naturally. In the proof we use vertex operator algebra relations for standard modules and coefficients of intertwining operators.
Quasi-reductive (bi)parabolic subalgebras in reductive Lie algebras.
We say that a finite dimensional Lie algebra is quasi-reductive if it has a linear form whose stabilizer for the coadjoint representation, modulo the center, is a reductive Lie algebra with a center consisting of semisimple elements. Parabolic subalgebras of a semisimple Lie algebra are not always quasi-reductive (except in types A or C by work of Panyushev). The classification of quasi-reductive parabolic subalgebras in the classical case has been recently achieved in unpublished work of Duflo,...
Quasispectra of solvable Lie algebra homomorphisms into Banach algebras
We propose a noncommutative holomorphic functional calculus on absolutely convex domains for a Banach algebra homomorphism π of a finite-dimensional solvable Lie algebra 𝔤 in terms of quasispectra σ(π). In particular, we prove that the joint spectral radius of a compact subset in a solvable operator Lie subalgebra coincides with the geometric spectral radius with respect to a quasispectrum.