On Right Alternative Algebras

1949 ◽  
Vol 50 (2) ◽  
pp. 318 ◽  
Author(s):  
A. A. Albert
Keyword(s):  
Alternative Algebras

scholarly journals Power and spherical series over real alternative *-algebras

2014 ◽  
Vol 63 (2) ◽  
pp. 495-532 ◽  
Author(s):  
Riccardo Ghiloni ◽  
Alessandro Perotti
Keyword(s):  
Alternative Algebras

scholarly journals The Torsion Product Property in Alternative Algebras

1996 ◽  
Vol 184 (1) ◽  
pp. 58-70 ◽  
Author(s):  
Edgar G. Goodaire ◽  
César Polcino Milies
Keyword(s):  
Product Property ◽  
Alternative Algebras

Mutations of Alternative Algebras

1994 ◽  
pp. 92-135
Author(s):  
Alberto Elduque ◽  
Hyo Chul Myung
Keyword(s):  
Alternative Algebras

scholarly journals Commutative Moufang loops and alternative algebras

2011 ◽  
Vol 333 (1) ◽  
pp. 1-13 ◽  
Author(s):  
Alexander N. Grishkov ◽  
Ivan P. Shestakov
Keyword(s):  
Alternative Algebras ◽  
Moufang Loops

Malcev–Poisson–Jordan algebras

2016 ◽  
Vol 15 (09) ◽  
pp. 1650159
Author(s):  
Malika Ait Ben Haddou ◽  
Saïd Benayadi ◽  
Said Boulmane
Keyword(s):  
Vector Space ◽  
Lie Algebras ◽  
Jordan Algebra ◽  
Jordan Algebras ◽  
Leibniz Rule ◽  
Malcev Algebra ◽  
Jordan Structure ◽  
Alternative Algebras

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.

Kupershmidt-(dual-)Nijenhuis structure on the alternative algebra with a representation

2020 ◽  
pp. 2150097
Author(s):  
Qinxiu Sun
Keyword(s):  
Alternative Algebra ◽  
Alternative Algebras ◽  
Alternative Formula

The aim of this paper is to study Kupershmidt-(dual-)Nijenhuis structures on alternative algebras with representations. The notion of a (dual-)Nijenhuis pair is introduced and it can generate a trivial deformation of an alternative algebra with a representation. We introduce the notion of a Kupershmidt-(dual-)Nijenhuis structure on an alternative algebra with a representation. Furthermore, we verify that Kupershmidt operators and Kupershmidt-(dual-)Nijenhuis structures can give rise to each other under some conditions. Finally, we study the notions of Rota–Baxter–Nijenhuis structures and alternative [Formula: see text]-matrix-Nijenhuis structures. Meanwhile, we investigate the relation between them.

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