Noncommutative homogeneous spaces: the matrix case

Abstract

Given a quantum subgroup $G\subset U_n$ and a number $k\le n$ we can form the homogeneous space $X=G/(G\cap U_k)$, and it follows from the Stone-Weierstrass theorem that $C(X)$ is the algebra generated by the last $n-k$ rows of coordinates on $G$. In the quantum group case the analogue of this basic result doesn't necessarily hold, and we discuss here its validity, notably with a complete answer in the group dual case. We focus then on the "easy quantum group" case, with the construction and study of several algebras associated to the noncommutative spaces of type $X=G/(G\cap U_k^{+})$.

24 pages

References in corpus (2)

• Liberation of orthogonal Lie groups
• Algebraic quantum permutation groups

Cited by in corpus (3)

• Liberations and twists of real and complex spheres
• A Connection between Easy Quantum Groups, Varieties of Groups and Reflection Groups
• Tannaka-Krein reconstruction and ergodic actions of easy quantum groups