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Complete descriptions of pseudo-Euclidean left-symmetric L-algebras and their pseudo-Euclidean modules.
- Source :
-
Journal of Algebra . Nov2024, Vol. 657, p600-637. 38p. - Publication Year :
- 2024
-
Abstract
- A pseudo-Euclidean left-symmetric algebra (A ,. , 〈 , 〉) is a left-symmetric algebra endowed with a non-degenerate symmetric bilinear form 〈 , 〉 such that left multiplications by any element of A are skew-symmetric with respect to 〈 , 〉. We recall that a pseudo-Euclidean Lie algebra (g , [ , ] , 〈 , 〉) is flat if and only if (g ,. , 〈 , 〉) , its underlying vector space endowed with the Levi-Civita product associated with 〈 , 〉 , is a pseudo-Euclidean left-symmetric algebra. In this paper, we study pseudo-Euclidean left-symmetric algebras (A ,. , 〈 , 〉) such that commutators of all elements of A are contained in the left annihilator of (A ,.) , these algebras will be called pseudo-Euclidean left-symmetric L -algebras. Next, we introduce and study pseudo-Euclidean modules of pseudo-Euclidean left-symmetric L -algebras. We develop double extension processes that allow us to have inductive descriptions of all pseudo-Euclidean left-symmetric L -algebras and of all its pseudo-Euclidean modules of any signature. This, in particular, improves some of the results obtained in [11]. [ABSTRACT FROM AUTHOR]
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 657
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 178188974
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2024.05.038