3 citations · 9 across the 10 of their papers we have counts for
11 papers
The Adams operators on connected graded Hopf algebras
Y. -Y. Li, G. -S. Zhou
The Adams operators on a Hopf algebra are the convolution powers of the identity map of . They are also called Hopf powers or Sweedler powers. It is a natural family of oper…
Coideal subalgebras of pointed and connected Hopf algebras
G. -S. Zhou
Let be a pointed Hopf algebra with abelian coradical. Let be left (or right) coideal subalgebras of that contain the coradical of . We show that has a…
The structure of connected (graded) Hopf algebras revisited
C. -C. Li, G. -S. Zhou
Let be a connected graded Hopf algebra over a field of characteristic zero and an arbitrary graded Hopf subalgebra of . We show that there is a family of homogeneous ele…
The structure of connected (graded) Hopf algebras
G. -S. Zhou, Y. Shen, D. -M. Lu
In this paper, we establish a structure theorem for connected graded Hopf algebras over a field of characteristic by claiming the existence of a family of homogeneous generator…
Skew Calabi-Yau property of normal extensions
G. -S. Zhou, Y. Shen, D. -M. Lu
We prove that the skew Calabi-Yau property is preserved under normal extension for locally finite positively graded algebras. We also obtain a homological identity which describes…
Ext-algebras of graded skew extensions
Y. Shen, X. Wang, G. -S. Zhou
In this paper, we study the Ext-algebras of graded skew extensions. For a connected graded algebra and a graded automorphism , we analyze the Yoneda product of the Ext-algeb…
Nakayama automorphisms of twisted tensor products
Y. Shen, G. -S. Zhou, D. -M. Lu
In this paper, we study homological properties of twisted tensor products of connected graded algebras. We focus on the Ext-algebras of twisted tensor products with a certain form…
Behavior of the Auslander condition with respect to regradings
G. -S. Zhou, Y. Shen, D. -M. Lu
We show that a noetherian ring graded by an abelian group of finite rank satisfies the Auslander condition if and only if it satisfies the graded Auslander condition. In addition,…
Lyndon words for Artin-Schelter regular algebras
G. -S. Zhou, D. -M. Lu
We show certain invariants of graded algebras of which all obstructions are Lyndon words and provide some methods to construct Artin-Schelter regular algebras from a closed set of…
Regularity criterion and classification for algebras of Jordan type
Y. Shen, G. -S. Zhou, D. -M. Lu
We show that Artin-Schelter regularity of a -graded algebra can be examined by its associated -graded algebra. We prove that there is exactly one class of…
Artin-Schelter regular algebras of dimension five with two generators
G. -S. Zhou, D. -M. Lu
We study and classify Artin-Schelter regular algebras of dimension five with two generators under an additional -grading by Hilbert driven Gröbner basis computations.…