Local properties of Schrödinger-Virasoro type Lie algebras and a full diamond thin Lie algebra

Let S V ( z ) be a class of Schrödinger-Virasoro type Lie algebras, where z ∈ Z . In this paper, we show that S V ( z ) is 2-local complete (namely, every 2-local derivation is a derivation) for almost all integers z's. We also introduce the notion of full diamond thin Lie algebras, and constru...

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Published inCommunications in algebra Vol. 52; no. 11; pp. 4650 - 4665
Main Authors Xia, Chunguang, Dong, Xiao, Wang, Dengyin, Zhang, Chi
Format Journal Article
LanguageEnglish
Published Abingdon Taylor & Francis 01.11.2024
Taylor & Francis Ltd
Subjects
2-local complete
2-local derivation
Derivation
Lie groups
Schrödinger-Virasoro type Lie algebras
thin Lie algebras
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Summary:Let S V ( z ) be a class of Schrödinger-Virasoro type Lie algebras, where z ∈ Z . In this paper, we show that S V ( z ) is 2-local complete (namely, every 2-local derivation is a derivation) for almost all integers z's. We also introduce the notion of full diamond thin Lie algebras, and construct an example F from S V ( − 1 ) . We completely determine the derivations of F by combinatoric techniques, and show that F is not 2-local complete.
ISSN:0092-7872
1532-4125
DOI:10.1080/00927872.2024.2356244