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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…
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…
Yang-Baxter equations and relative Rota-Baxter operators for left-Alia algebras associated to invariant theory
Kang Chuangchuang, Liu Guilai, Shizhuo Yu
Left-Alia algebras are a class of algebras with symmetric Jacobi identities. They contain several typical types of algebras as subclasses, and are closely related to the invariant…
Manin triples and bialgebras of Left-Alia algebras associated to invariant theory
Kang Chuangchuang, Liu Guilai, Wang Zhuo +1
A left-Alia algebra is a vector space together with a bilinear map satisfying symmetric Jocobi identity. Motivated by invariant theory, we first construct a class of left-Alia alge…
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…
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…
3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivations
Ruipu Bai, Shuai Hou, Chuangchuang Kang
In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if is an -dimensional 3-Lie algebra with an involutive derivation , the…
The infinite dimensional Unital 3-Lie Poisson algebra
Chuangchuang Kang, Ruipu Bai, Yingli Wu
From a commutative associative algebra , the infinite dimensional unital 3-Lie Poisson algebra~~is constructed, which is also a canonical Nambu 3-Lie algebra, and…