Structure of a class of Lie algebras of Block type

2011/02/25 by Chunguang Xia, Xia, Chunguang, Taijie You +3
Mathematics · #Advanced Algebra and Geometry #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1102.5183

openalex publication_date 2011/02/25 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Let \BB be a class of Lie algebras of Block type with basis \L_\a,i|\a,i∈\Z, i≥ 0\ and relations [L_\a,i,L_\b,j]=(\b(i+q)-\a(j+q))L_\a+\b,i+j, where q is a positive integer. In this paper, it is shown that \BB are different from each other for distinct positive integers q's. The automorphism groups, the derivation algebras and the central extensions of all \BB are also uniformly and explicitly described, which generalize some previous results.

Related

• Derivations and automorphisms of a Lie algebra of Block type
• The Lie conformal algebra of a Block type Lie algebra
• Structure of the Lie algebras related to those of block
• Generalizations of the Block algebras
• Block type Lie algebras and their representations