Chuangchuang Kang
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View article: Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras
Matched pairs and double construction bialgebras of (transposed) Poisson 3-Lie algebras Open
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 Poisson 3-Lie algebras are constructed on direct sums and te…
View article: Manin Triples, Bialgebras and Yang-Baxter Equation of $A_3$-Associative Algebras
Manin Triples, Bialgebras and Yang-Baxter Equation of $A_3$-Associative Algebras Open
View article: Yang-Baxter Equations and Relative Rota-Baxter Operators for Left-Alia Algebras Associated to Invariant Theory
Yang-Baxter Equations and Relative Rota-Baxter Operators for Left-Alia Algebras Associated to Invariant Theory Open
View article: Universal enveloping algebras of weighted differential Poisson algebras
Universal enveloping algebras of weighted differential Poisson algebras Open
The $λ$-differential operators and modified $λ$-differential operators are generalizations of classical differential operators. This paper introduces the notions of $λ$-differential Poisson ($λ$-DP for short) algebras and modified $λ$-diff…
View article: Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory
Manin Triples and Bialgebras of Left-Alia Algebras Associated with Invariant Theory Open
A left-Alia algebra is a vector space together with a bilinear map satisfying the symmetric Jacobi identity. Motivated by invariant theory, we first construct a class of left-Alia algebras induced by twisted derivations. Then, we introduce…
View article: Universal Enveloping Algebras of Weighted Differential Poisson Algebras
Universal Enveloping Algebras of Weighted Differential Poisson Algebras Open
View article: Nijenhuis operators on 2D pre-Lie algebras and 3D associative algebras
Nijenhuis operators on 2D pre-Lie algebras and 3D associative algebras Open
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 operators, we obtain solutions of the classical Yang-Baxter equatio…
View article: Manin triples associated to $n$-Lie bialgebras
Manin triples associated to $n$-Lie bialgebras Open
In this paper, we study the Manin triples associated to $n$-Lie bialgebras. We introduce the concept of operad matrices for $n$-Lie bialgebras. In particular, by studying a special case of operad matrices, it leads to the notion of local c…
View article: Manin Triples Associated to N-Lie Bialgebras
Manin Triples Associated to N-Lie Bialgebras Open
View article: Polyubles, Poisson homogeneous spaces and multi-flag varieties
Polyubles, Poisson homogeneous spaces and multi-flag varieties Open
A polyuble of a Manin triple can be regarded as the ``$n$-th power'' of it, which plays an important rule in the study of Poisson geometry, mathematical physics and Lie theory. In this paper, we first construct an isomorphism between the $…
View article: 3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivations
3-Lie bialgebras and 3-pre-Lie algebras induced by involutive derivations Open
In this paper, we study the structure of 3-Lie algebras with involutive derivations. We prove that if $A$ is an $m$-dimensional 3-Lie algebra with an involutive derivation $D$, then there exists a compatible 3-pre-Lie algebra $(A, \{ , , ,…
View article: The infinite dimensional Unital 3-Lie Poisson algebra
The infinite dimensional Unital 3-Lie Poisson algebra Open
From a commutative associative algebra $A$, the infinite dimensional unital 3-Lie Poisson algebra~$\mathfrak{L}$~is constructed, which is also a canonical Nambu 3-Lie algebra, and the structure of $\mathfrak{L}$ is discussed. It is proved …