8 papers
An Alternative Proof of Dilworth's Theorem via Local Chain Merges
Tao Zhang
Several elegant proofs of Dilworth's theorem for finite posets already exist in the literature. In this note, we present an alternative inductive proof using a local legal merge le…
Non-abelian extensions and Wells exact sequences of Bol algebras
Jingzi Zhang, Tao Zhang
The aim of this paper is to explore non-abelian extensions of Bol algebras and to study the extensibility of a pair of automorphisms within these non-abelian extensions. We begin b…
Cohomology and automorphisms of Com-PreLie algebras
Tao Zhang, Ying-Hua Lu
This paper introduces the concept of representations for Com-PreLie algebras and develops corresponding cohomology theories, examining how cohomology groups can be applied in the c…
Cohomology and automorphisms for a matched pair of 3-Lie algebras
Tao Zhang, Jingzi Zhang
We begin by reviewing the definition of 3-Lie algebras and the fundamental concepts of matched pairs. Subsequently, we introduce the representation theory of matched pairs and defi…
Wells exact sequence for automorphisms and derivations of Leibniz 2-algebras
Wei Zhong, Tao Zhang
In this paper, we investigate the inducibility of pairs of automorphisms and derivations in Leibniz 2-algebras. To begin, we provide essential background information on Leibniz 2-a…
Non-abelian extensions and automorphisms of post-Lie algebras
Lisi Bai, Tao Zhang
In this paper, we introduce the concepts of crossed modules of post-Lie algebras and cat-post-Lie algebras. It is proved that these two concepts are equivalent to each other. S…
Lie triple 2-algebras
Tao Zhang, Zhang-Ju Liu
We invent a new cohomology theory for Lie triple algebras. Using this cohomology, we introduce the notions of 2-term -triple algebras and Lie triple 2-algebras. We prove…
Deformations and extensions of homotopy associative algebras
Tao Zhang
The representation and the cohomology theory of associative 2-algebras are developed. We study the deformations and abelian extensions of associative 2-algebras in details.