On the Frattini subalgebra of a Malcev algebra

1981 ◽  
Vol 37 (1) ◽  
pp. 306-315 ◽  
Author(s):  
Alfy Abd el Malek
Keyword(s):  
Malcev Algebra ◽  
Frattini Subalgebra

scholarly journals The simple non-Lie Malcev algebra as a Lie–Yamaguti algebra

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

scholarly journals An N=8 superaffine Malcev algebra and its N=8 Sugawara

2001 ◽  
Vol 291 (2-3) ◽  
pp. 95-102 ◽  
Author(s):  
H.L. Carrion ◽  
M. Rojas ◽  
F. Toppan
Keyword(s):  
Malcev Algebra

scholarly journals Extension of Malcev Algebra and Applications to Gravity

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

scholarly journals Corrigendum et addendum: the Frattini subalgebra of a Bernstein algebra

1994 ◽  
Vol 37 (3) ◽  
pp. 519-520
Author(s):  
Jesús Laliena
Keyword(s):  
Maximal Subalgebra ◽  
Frattini Subalgebra ◽  
Bernstein Algebra

In a previous paper it is supposed that if A is a Bernstein algebra, every maximal subalgebra, M, verifies that dim M = dim A − 1. This is not true in general. Therefore Proposition 2 in this paper is not correct. However other results there, where this assertion was used, are correct but their proofs need some modifications now.

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.

scholarly journals LIE 3-ALGEBRA AND SUPER-AFFINIZATION OF SPLIT-OCTONIONS

2011 ◽  
Vol 26 (35) ◽  
pp. 2663-2675 ◽  
Author(s):  
HECTOR L. CARRIÓN ◽  
SERGIO GIARDINO
Keyword(s):  
Gauge Theory ◽  
Structure Tensor ◽  
Malcev Algebra ◽  
Single Operation ◽  
Structure Constants ◽  
Split Octonions

The purpose of this study is to extend the concept of a generalized Lie 3-algebra, known to the divisional algebra of the octonions 𝕆, to split-octonions 𝕊𝕆, which is non-divisional. This is achieved through the unification of the product of both of the algebras in a single operation. Accordingly, a notational device is introduced to unify the product of both algebras. We verify that 𝕊𝕆 is a Malcev algebra and we recalculate known relations for the structure constants in terms of the introduced structure tensor. Finally we construct the manifestly supersymmetric [Formula: see text] affine superalgebra. An application of the split Lie 3-algebra for a Bagger and Lambert gauge theory is also discussed.

scholarly journals Enveloping Algebras of the Nilpotent Malcev Algebra of Dimension Five

2009 ◽  
Vol 13 (4) ◽  
pp. 407-425 ◽  
Author(s):  
Murray R. Bremner ◽  
Hamid Usefi
Keyword(s):  
Enveloping Algebras ◽  
Malcev Algebra
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