arXiv subjects

Kang Chuangchuang

Publications and source records attributed to Kang Chuangchuang.

4 recordsLinked to original sources

arXiv2025

Classification of Transposed Poisson 3-Lie algebras of dimension 3

Transposed Poisson $3$-Lie algebra is a dual notion of Nambu-Poisson algebra of order 3. In this paper, we explicitly determine all $\frac{1}{3}$-derivations and automorphisms of the unique nontrivial $3$-dimensional complex $3$-Lie algebra $(A_3,[\cdot,\cdot,\cdot])$. Based on the one-one correspondence between $\frac{1}{3}$-derivations and transposed Poisson 3-Lie algebras, up to isomorphism, we classify transposed Poisson $3$-Lie algebras of dimension $3$ under the case that $L_{e_1}$ is trivial over the complex field $\mathbb{C}$.

math.RA↗

arXiv2024

Yang-Baxter equations and relative Rota-Baxter operators for left-Alia algebras associated to invariant theory

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 theory. In this paper, we study the construction theory of left-Alia bialgebras. We introduce the notion of the left-Alia Yang-Baxter equation. We show that an antisymmetric solution of the left-Alia Yang-Baxter equation gives rise to a left-Alia bialgebra that we call triangular. The notions of relative Rota-Baxter operators of left-Alia algebras and pre-left-Alia algebras are introduced to provide antisymmetric solutions of the left-Alia Yang-Baxter equation.

math.RA↗

arXiv2024

Manin triples and bialgebras of Left-Alia algebras associated to invariant theory

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 algebras induced by twisted derivations. Then, we introduce the notion of Manin triples and bialgebras of left-Alia algebras. Via specific matched pairs of left-Alia algebras, we figure out the equivalence between Manin triples and bialgebras of left-Alia algebras.

math.RA↗

arXiv2023

From $\mathcal{O}$-operators of 3-Dimensional 3-Lie algebras to 3-Pre-Lie algebras

In this paper, we explicitly determine all $\mathcal{O}$-operators with respect to the adjoint representation of 3-dimensional complex 3-Lie algebras. Furthermore, we provide the induced 3-Pre-Lie algebra structures and the corresponding solutions of the 3-Lie classical Yang-Baxter equation in the 6-dimensional 3-Lie algebras $A\ltimes_{\mathrm{ad}^*} A^*$.

math-ph↗