22 citations · 69 across the 13 of their papers we have counts for
13 papers
Homological unimodularity and Calabi-Yau condition for Poisson algebras
Jiafeng Lü, Xingting Wang, Guangbin Zhuang
In this paper, we show that the twisted Poincaré duality between Poisson homology and cohomology can be derived from the Serre invertible bimodule. This gives another definition of…
DG Poisson algebra and its universal enveloping algebra
Jiafeng Lu, Xingting Wang, Guangbin Zhuang
In this paper, we introduce the notions of differential graded (DG) Poisson algebra and DG Poisson module. Let be any DG Poisson algebra. We construct the universal enveloping…
Primitive Cohomology of Hopf algebras
D. -G. Wang, J. J. Zhang, G. Zhuang
Primitive cohomology of a Hopf algebra is defined by using a modification of the cobar construction of the underlying coalgebra. Among many of its applications, two classifications…
A note on the duality between Poisson homology and cohomology
Jiafeng Lü, Xingting Wang, Guangbin Zhuang
For a Poisson algebra , by studying its universal enveloping algebra , we prove a duality theorem between Poisson homology and cohomology of .
Universal enveloping algebras of Poisson Ore extensions
Jiafeng Lü, Xingting Wang, Guangbin Zhuang
We prove that the universal enveloping algebra of a Poisson-Ore extension is a length two iterated Ore extension of the original universal enveloping algebra. As consequences, we o…
Universal enveloping algebras of Poisson Hopf algebras
Jiafeng Lü, Xingting Wang, Guangbin Zhuang
For a Poisson algebra , by exploring its relation with Lie-Rinehart algebras, we prove a Poincaré-Birkoff-Witt theorem for its universal enveloping algebra . Some general p…
Connected Hopf algebras and iterated Ore extensions
K. A. Brown, S. O'Hagan, J. J. Zhang +1
We investigate when a skew polynomial extension T = R[x; σ, δ] of a Hopf algebra R admits a Hopf algebra structure, substantially generalising a theorem of Panov. When this constru…
Connected Hopf algebras of Gelfand-Kirillov dimension four
D. -G. Wang, J. J. Zhang, G. Zhuang
We classify connected Hopf algebras of Gelfand-Kirillov dimension 4 over an algebraic closed field of characteristic zero.
Coassociative Lie algebras
D. -G. Wang, J. J. Zhang, G. Zhuang
A coassociative Lie algebra is a Lie algebra equipped with a coassociative coalgebra structure satisfying a compatibility condition. The enveloping algebra of a coassociative Lie a…
Properties of pointed and connected Hopf algebras of finite Gelfand-Kirillov dimension
Guangbin Zhuang
Let be a pointed Hopf algebra. We show that under some mild assumptions and its associated graded Hopf algebra $\gr H$ have the same Gelfand-Kirillov dimension. As an appli…
Hopf algebras of GK-dimension two with vanishing Ext-group
D. -G. Wang, J. J. Zhang, G. Zhuang
We construct and study a family of finitely generated Hopf algebra domains of Gelfand-Kirillov dimension two such that $\Ext^1_H(k,k)=0$. Consequently, we answer a question of…
Lower bounds of Growth of Hopf algebras
D. -G. Wang, J. J. Zhang, G. Zhuang
Some lower bounds of GK-dimension of Hopf algebras are given.
Existence of Hopf subalgebras of GK-dimension two
Guangbin Zhuang
Let be a pointed Hopf algebra over an algebraically closed field of characteristic zero. If is a domain with finite Gelfand-Kirillov dimension greater than or equal to two,…