We begin with some terminology and background, in particular we define the notions of Hopf
algebras and quantum groups. Let H be the algebra of functions of a Lie group G. Then the …

Let H be a Hopf algebra that is ℤ-graded as an algebra. We provide sufficient conditions for
a 2-cocycle twist of H to be a Zhang twist of H. In particular, we introduce the notion of a …

We introduce the concept of a universal quantum linear semigroupoid (UQSGd), which is a
weak bialgebra that coacts on a (not necessarily connected) graded algebra A universally …

This is survey of results that extend notions of the classical invariant theory of linear actions
by finite groups on k [x1,..., xn] to the setting of finite group or Hopf algebra H actions on an …

We introduce the notion of quantum-symmetric equivalence of two connected graded
algebras, based on Morita–Takeuchi equivalences of their universal quantum groups, in the …

We show that $ A_s (n) $, the coordinate algebra of Wang's quantum permutation group, is
Calabi-Yau of dimension $3 $ when $ n\geq 4$, and compute its Hochschild cohomology …

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 …

We define the universal quantum group H that preserves a pair of Hopf comodule maps,
whose underlying vector space maps are preregular forms defined on dual vector spaces …

Abstract For any Koszul Artin–Schelter regular algebra A, we consider the universal Hopf
algebra aut _ (A) coacting on A, introduced by Manin. To study the representations (ie finite …

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 …