7 papers · 1 filter
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.