22 citations · 57 across the 27 of their papers we have counts for
27 papers
Universal Enveloping Algebras of Hom-Lie Algebras with -Derivations
Zhangqiuyu Jiang, Chuangchuang Kang, Jiafeng Lü
In this paper, we construct nonunital universal enveloping Hom-associative algebras for multiplicative Hom-Lie algebras equipped with -derivations. We prove that the prescribed…
Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras
Kecheng Zhou, Chuangchuang Kang, Jiafeng Lü
Double construction bialgebras for Poisson 3-Lie algebras and transposed Poisson 3-Lie algebras are defined and studied using matched pairs. Poisson 3-Lie algebras and transposed P…
Universal enveloping H-pseudoalgebras of DGP pseudoalgebras
Ying Chen, Jiafeng Lü, Jiaqun Wei
The notions of Poisson -pseudoalgebras are generalizations of Poisson algebras in a pseudotensor category . This paper introduces an analogue of Poisson-O…
Manin triples, bialgebras and Yang-Baxter equation of -associative algebras
Yaxi Jiang, Chuangchuang Kang, Jiafeng Lü
-associative algebra is a generalization of associative algebra and is one of the four remarkable types of Lie-admissible algebras, along with associative algebra, left-symmet…
Universal enveloping algebras of weighted differential Poisson algebras
Ying Chen, Chuangchuang Kang, Jiafeng Lü
The -differential operators and modified -differential operators are generalizations of classical differential operators. This paper introduces the notions of -differentia…
Relative torsionfreeness and Frobenius extensions
Yanhong Bao, Jiafeng Lü, Zhibing Zhao
Let be a Frobenius extension with centrally projective over . We show that if is a Wakamatsu tilting module then so is , and the natural ring…
Classification of Transposed Poisson 3-Lie algebras of dimension 3
Jiang Yaxi, Kang Chuangchuang, Lü Jiafeng
Transposed Poisson -Lie algebra is a dual notion of Nambu-Poisson algebra of order 3. In this paper, we explicitly determine all -derivations and automorphisms of t…
From -operators of 3-Dimensional 3-Lie algebras to 3-Pre-Lie algebras
Cheng Ziying, Kang Chuangchuang, Lü Jiafeng
In this paper, we explicitly determine all -operators with respect to the adjoint representation of 3-dimensional complex 3-Lie algebras. Furthermore, we provide the i…
Nijenhuis operators on 2D pre-Lie algebras and 3D associative algebras
Xiaoguang Zou, Xiang Gao, Chuangchuang Kang +1
In this paper, we describe all Nijenhuis operators on 2-dimensional complex pre-Lie algebras and 3-dimensional complex associative algebras. As an application, using these operator…
Manin triples associated to -Lie bialgebras
Ying Chen, Chuangchuang Kang, Jiafeng Lü +1
In this paper, we study the Manin triples associated to -Lie bialgebras. We introduce the concept of operad matrices for -Lie bialgebras. In particular, by studying a special…
How to construct Gorenstein projective modules relative to complete duality pairs over Morita rings
Yajun Ma, Jiafeng Lü, Huanhuan Li +1
Let be a Morita ring with .We first study how to construct (comple…
Frobenius functors and Gorenstein projective precovers
Jiangsheng Hu, Huanhuan Li, Jiafeng Lu +1
We establish relations between Gorenstein projective precovers linked by Frobenius functors. This is motivated by an open problem that how to find general classes of rings for whic…
The structures on the universal enveloping algebras of differential graded Poisson Hopf algebras
Mengtian Guo, Xianguo Hu, Jiafeng Lu +1
In this paper, the so-called differential graded (DG for short) Poisson Hopf algebra is introduced, which can be considered as a natural extension of Poisson Hopf algebras in the d…
PBW-basis for universal enveloping algebras of differential graded Poisson algebras
Xianguo Hu, Jiafeng Lu, Xingting Wang
For any differential graded (DG for short) Poisson algebra given by generators and relations, we give a "formula" for computing the universal enveloping algebra of . M…
A note on the bijectivity of antipode of a Hopf algebra and its applications
Jiafeng Lv, Sei-Qwon Oh, Xingting Wang +1
Certain sufficient homological and ring-theoretical conditions are given for a Hopf algebra to have bijective antipode with applications to noetherian Hopf algebras regarding their…
Enveloping algebras of double Poisson-Ore extensions
Jiafeng Lü, Sei-Qwon Oh, Xingting Wang +1
It is proved that the Poisson enveloping algebra of a double Poisson-Ore extension is an iterated double Ore extension. As an application, properties that are preserved under itera…
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…
Nakayama automorphism of a class of graded algebras
J. -F. Lü, X. -F. Mao, J. J. Zhang
The Nakayama automorphism of a class of connected graded Artin-Schelter regular algebras is calculated explicitly.
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…
Nakayama automorphism and applications
Jiafeng Lu, Xuefeng Mao, James J. Zhang
Nakayama automorphism is used to study group actions and Hopf algebra actions on Artin-Schelter regular algebras of global dimension three.
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 differential graded Poisson algebras
Jiafeng Lü, Xingting Wang, Guangbin Zhuang
In this paper, we introduce the notion of differential graded Poisson algebra and study its universal enveloping algebra. From any differential graded Poisson algebra , we const…
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…