arXiv subjects

Jingzi Zhang

Publications and source records attributed to Jingzi Zhang.

2 recordsLinked to original sources

arXiv2025

Non-abelian extensions and Wells exact sequences of Bol algebras

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 by researching non-abelian extensions of Bol algebras and categorizing them based on non-abelian cohomology groups. Additionally, we discuss the conditions under which a pair of automorphisms can be extended in the context of non-abelian extensions of Bol algebras and derive the corresponding Wells exact sequences.

math.RA↗

arXiv2025

Cohomology and automorphisms for a matched pair of 3-Lie algebras

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 define the semidirect product. Building on this foundation, we define the low-dimensional cohomology groups of matched pairs. In addition, we explore the infinitesimal deformations and abelian extensions of matched pairs. Finally, we examine the inducibility of automorphisms of matched pairs and present related results through the Wells exact sequence.

math.RA↗