malcev algebra
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2019 ◽  
Vol 67 (7) ◽  
pp. 1900027
Author(s):  
Junpei Harada
Keyword(s):  

2019 ◽  
Vol 09 (05) ◽  
pp. 632-640
Author(s):  
进圆 李

2016 ◽  
Vol 15 (09) ◽  
pp. 1650159
Author(s):  
Malika Ait Ben Haddou ◽  
Saïd Benayadi ◽  
Said Boulmane

Malcev–Poisson–Jordan algebra (MPJ-algebra) is defined to be a vector space endowed with a Malcev bracket and a Jordan structure which are satisfying the Leibniz rule. We describe such algebras in terms of a single bilinear operation, this class strictly contains alternative algebras. For a given Malcev algebra [Formula: see text], it is interesting to classify the Jordan structure ∘ on the underlying vector space of [Formula: see text] such that [Formula: see text] is an MPJ-algebra (∘ is called an MPJ-structure on Malcev algebra [Formula: see text]. In this paper we explicitly give all MPJ-structures on some interesting classes of Malcev algebras. Further, we introduce the concept of pseudo-Euclidean MPJ-algebras (PEMPJ-algebras) and we show how one can construct new interesting quadratic Lie algebras and pseudo-Euclidean Malcev (non-Lie) algebras from PEMPJ-algebras. Finally, we give inductive descriptions of nilpotent PEMPJ-algebras.


2014 ◽  
Vol 405 ◽  
pp. 38-68 ◽  
Author(s):  
Alexandr I. Kornev
Keyword(s):  

2012 ◽  
Vol 140 (9) ◽  
pp. 3049-3054
Author(s):  
I. P. Shestakov ◽  
A. I. Kornev
Keyword(s):  

2012 ◽  
Vol 358 ◽  
pp. 269-291 ◽  
Author(s):  
Murray R. Bremner ◽  
Andrew Douglas
Keyword(s):  

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