Shizhuo Yu
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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: 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
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 …
View article: Manin triples and bialgebras of Left-Alia algebras associated to invariant theory
Manin triples and bialgebras of Left-Alia algebras associated to invariant theory Open
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…
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: 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: Configuration Poisson Groupoids of Flags
Configuration Poisson Groupoids of Flags Open
Let $G$ be a connected complex semi-simple Lie group and ${\mathcal {B}}$ its flag variety. For every positive integer $n$, we introduce a Poisson groupoid over ${{\mathcal {B}}}^n$, called the $n$th total configuration Poisson groupoid of…
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: Configuration Poisson groupoids of flags
Configuration Poisson groupoids of flags Open
Let $G$ be a connected complex semi-simple Lie group and ${\mathcal{B}}$ its flag variety. For every positive integer $n$, we introduce a Poisson groupoid over ${\mathcal{B}}^n$, called the $n$th total configuration Poisson groupoid of fla…
View article: Bott-Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces
Bott-Samelson atlases, total positivity, and Poisson structures on some homogeneous spaces Open
Let $G$ be a connected and simply connected complex semisimple Lie group. For a collection of homogeneous $G$-spaces $G/Q$, we construct a finite atlas ${\mathcal{A}}_{\rm BS}(G/Q)$ on $G/Q$, called the Bott-Samelson atlas, and we prove th…
View article: On the Frobenius splitting of the basic affine space
On the Frobenius splitting of the basic affine space Open
View article: On the Knutson-Woo-Yong maps and some poisson homogeneous spaces
On the Knutson-Woo-Yong maps and some poisson homogeneous spaces Open
View article: On a class of Poisson structures from Lie theory
On a class of Poisson structures from Lie theory Open
资助项目 摘要 Poisson 几何是 Hamilton 力学及辛流形紧化自然的研究框架.本文介绍了一类与 Lie 理论有 关的 Poisson 流形.这类 Poisson 流形的构造来自于量子群, 并与分次扩张 Poisson
View article: Data from: Two influential primate classifications logically aligned
Data from: Two influential primate classifications logically aligned Open
Classifications and phylogenies of perceived natural entities change in the light of new evidence. Taxonomic changes, translated into Code-compliant names, frequently lead to name:meaning dissociations across succeeding treatments. Classif…