Triple Lie Systems Associated with (−1, 1) Algebras

We introduce a Lie triple system associated with the central isotope of (− 1, 1)-algebra. The associator ideal of (−1, 1)-algebra is nilpotent if and only if the Lie triple system is nilpotent. The relationship of the constructed Lie triple system with other known Lie triple systems is discussed....

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Bibliographic Details
Published in:Russian mathematics 2020-03, Vol.64 (3), p.72-75
Main Authors: Borisova, L. R., Pchelintsev, S. V.
Format: Article
Language:English
Subjects:
Algebra
Brief Communications
Mathematics
Mathematics and Statistics
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Summary:We introduce a Lie triple system associated with the central isotope of (− 1, 1)-algebra. The associator ideal of (−1, 1)-algebra is nilpotent if and only if the Lie triple system is nilpotent. The relationship of the constructed Lie triple system with other known Lie triple systems is discussed.
ISSN:1066-369X
1934-810X
DOI:10.3103/S1066369X2003007X