We investigate homological and ring-theoretic properties of universal quantum linear groups
that coact on Artin-Schelter regular algebras A (n) of global dimension 2, especially with …

We study the 10 noncommutative spheres obtained by liberating, twisting, and liberating+
twisting the real and complex spheres SRN− 1, SCN− 1. At the axiomatic level, we show …

Suppose that a compact quantum group Q acts faithfully on a smooth, compact, connected
manifold M, ie has a C⁎(co)-action α on C (M), such that α (C∞(M))⊆ C∞(M, Q) and the …

It is not very common to embark upon the assiduous project of writing a book on a research
topic within 5 years of its inception. One usually needs somewhat longer time to let the dust …

Suppose that a compact quantum group QQ acts faithfully on a smooth, compact, connected
manifold M, ie has a C*(co)-action α on C (M), such that the action α is isometric in the sense …

We discuss the liberation question, in the homogeneous space setting. Our first series of
results concerns the axiomatization and classification of the families of compact quantum …

We prove the existence of a quantum isometry groups for new classes of metric spaces:(i)
geodesic metrics for compact connected Riemannian manifolds (possibly with boundary) …

We discuss the liberation question, in the homogeneous space setting. Our first series of
results concerns the axiomatization and classification of the families of compact quantum …

Suppose that a compact quantum group $\clq $ acts faithfully on a smooth, compact,
connected manifold $ M $, ie has a $ C^* $(co)-action $\alpha $ on $ C (M) $, such that the …

Let $ X $ be a noncommutative real compact algebraic manifold, in the sense that $ C (X)=
C^*(x_1,\ldots, x_N| x_i= x_i^*, f_\alpha (x_1,\ldots, x_N)= 0) $, with $ f_\alpha\in\mathbb R< …