Structure of n-Lie Algebras with Involutive Derivations
Joint Authors
Bai, Ruipu
Hou, Shuai
Gao, Yansha
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2018, Issue 2018 (31 Dec. 2018), pp.1-9, 9 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2018-09-02
Country of Publication
Egypt
No. of Pages
9
Main Subjects
Abstract EN
We study the structure of n-Lie algebras with involutive derivations for n≥2.
We obtain that a 3-Lie algebra A is a two-dimensional extension of Lie algebras if and only if there is an involutive derivation D on A=A1 ∔ A-1 such that dim A1=2 or dim A-1=2, where A1 and A-1 are subspaces of A with eigenvalues 1 and -1, respectively.
We show that there does not exist involutive derivations on nonabelian n-Lie algebras with n=2s for s≥1.
We also prove that if A is a (2s+2)-dimensional (2s+1)-Lie algebra with dim A1=r, then there are involutive derivations on A if and only if r is even, or r satisfies 1≤r≤s+2.
We discuss also the existence of involutive derivations on (2s+3)-dimensional (2s+1)-Lie algebras.
American Psychological Association (APA)
Bai, Ruipu& Hou, Shuai& Gao, Yansha. 2018. Structure of n-Lie Algebras with Involutive Derivations. International Journal of Mathematics and Mathematical Sciences،Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1173516
Modern Language Association (MLA)
Bai, Ruipu…[et al.]. Structure of n-Lie Algebras with Involutive Derivations. International Journal of Mathematics and Mathematical Sciences No. 2018 (2018), pp.1-9.
https://search.emarefa.net/detail/BIM-1173516
American Medical Association (AMA)
Bai, Ruipu& Hou, Shuai& Gao, Yansha. Structure of n-Lie Algebras with Involutive Derivations. International Journal of Mathematics and Mathematical Sciences. 2018. Vol. 2018, no. 2018, pp.1-9.
https://search.emarefa.net/detail/BIM-1173516
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-1173516