Search results for "17B37"
showing 5 items of 5 documents
Quantization of Poisson Lie Groups and Applications
1996
LetG be a connected Poisson-Lie group. We discuss aspects of the question of Drinfel'd:can G be quantized? and give some answers. WhenG is semisimple (a case where the answer isyes), we introduce quantizable Poisson subalgebras ofC ∞(G), related to harmonic analysis onG; they are a generalization of F.R.T. models of quantum groups, and provide new examples of quantized Poisson algebras.
Quantum Toda Lattice: a Challenge for Representation Theory
2021
Quantum Toda lattice may solved by means of the Representation Theory of semisimple Lie groups, or alternatively by using the technique of the Quantum Inverse Scattering Method. A comparison of the two approaches, which is the purpose of the present review article, sheds a new light on Representation Theory and leads to a number of challenging questions.
Invariant Markov semigroups on quantum homogeneous spaces
2019
Invariance properties of linear functionals and linear maps on algebras of functions on quantum homogeneous spaces are studied, in particular for the special case of expected coideal *-subalgebras. Several one-to-one correspondences between such invariant functionals are established. Adding a positivity condition, this yields one-to-one correspondences of invariant quantum Markov semigroups acting on expected coideal *-subalgebras and certain convolution semigroups of states on the underlying compact quantum group. This gives an approach to classifying invariant quantum Markov semigroups on these quantum homogeneous spaces. The generators of these semigroups are viewed as Laplace operators …
The Reasonable Effectiveness of Mathematical Deformation Theory in Physics
2019
This is a brief reminder, with extensions, from a different angle and for a less specialized audience, of my presentation at WGMP32 in July 2013, to which I refer for more details on the topics hinted at in the title, mainly deformation theory applied to quantization and symmetries (of elementary particles).
The hidden group structure of quantum groups: strong duality, rigidity and preferred deformations
1994
A notion of well-behaved Hopf algebra is introduced; reflexivity (for strong duality) between Hopf algebras of Drinfeld-type and their duals, algebras of coefficients of compact semi-simple groups, is proved. A hidden classical group structure is clearly indicated for all generic models of quantum groups. Moyal-product-like deformations are naturally found for all FRT-models on coefficients andC∞-functions. Strong rigidity (H bi 2 ={0}) under deformations in the category of bialgebras is proved and consequences are deduced.