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 …

We present a rich source of Hopf algebras starting from a cofinite central extension of a
Noetherian Hopf algebra and a subgroup of the algebraic group of characters of the central …

We discuss the question of whether the global dimension is a monoidal invariant for Hopf
algebras, in the sense that if two Hopf algebras have equivalent monoidal categories of …

We compute the Hochschild and Gerstenhaber–Schack cohomological dimensions of the
universal cosovereign Hopf algebras, when the matrix of parameters is a generic …

In this paper, we prove that the quantum groups 𝒢 (A, B) introduced by Mrozinski in [C.
Mrozinski, Quantum groups of GL (2) representation type, J. Noncommut. Geom. 8 (1)(2014) …

Let A be a Hopf algebra and B a graded twisting of A by a finite abelian group Γ. Then,
categories of comodules over A and B are equivalent (but they are not necessarily …

A note on the bijectivity of the antipode of a Hopf algebra and its applications Page 1
PROCEEDINGS OF THE AMERICAN MATHEMATICAL SOCIETY Volume 146, Number 11 …

While it was identified that the growth of any connected Hopf algebras is either a positive
integer or infinite, we have yet to determine the Gelfand–Kirillov (GK) dimension of a given …

We know that given a connected Hopf algebra H, the universal enveloping algebra U (P (H))
embeds in H as a Hopf subalgebra. Depending on P (H), we show that there may be another …

• True for A= kΓ, A finite-dimensional (both dimensions are either 0 in the cosemisimple case
by Larson-Radford, or∞), and probably for A= O (G), with G connected reductive algebraic …