Invariant Markov semigroups on the quantum homogeneous spaces

Dyskretna analiza harmoniczna i niekomutatywna probabilistyka
Osoba referująca: 
Xumin Wang (Universite Bourgogne Franche Comte)
Data spotkania seminaryjnego: 
czwartek, 24. Styczeń 2019 - 10:15

We obtained some 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 classical sphere $S^{N-1}$, the free sphere $S^{N-1}_+$, and the half-liberated sphere $S^{N-1}_*$ are considered as examples. On these spheres, we classifying the generators of the invariant quantum Markov semigroups by calculating their eigenvalues and eigenvector spaces. The generators obtained in this way can naturally be viewed as Laplace operators on these spaces.

Referat odbędzie się w ramach projektu Polonium, współfinansowanego przez Narodową Agencję Wymiany Akademickiej (NAWA).