Continuity of derivations on Mal'cev H*-algebras

1991 ◽  
Vol 110 (3) ◽  
pp. 455-459 ◽  
Author(s):  
Borut Zalar
Keyword(s):  
Lie Algebras ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Alternative Algebras ◽  
Mal’Cev Algebras ◽  
Long Time

A long time ago the concept of H*-algebra was introduced by Ambrose in [1] where the structure of complex associative H*-algebras was given. Since then this theory was extended to such classical types of non-associative algebras as alternative algebras (in [6]), Jordan algebras (in [5, 13, 14]), non-commutative Jordan algebras (in [5]), Lie algebras (in [3, 9, 10]) and Mal'cev algebras (in [2]).

Some Lie Admissible Algebras

1962 ◽  
Vol 14 ◽  
pp. 287-292 ◽  
Author(s):  
P. J. Laufer ◽  
M. L. Tomber
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Alternative Algebras

Several studies have been made to obtain larger classes of non-associative algebras from classes of algebras with a known structure. Thus, we have right alternative algebras (2)* and non-commutative Jordan algebras (6), (7), (8), and (9). These algebras are defined by a subset of the set of identities of the algebras from which they derive their names. Also, Albert (1), among others has studied Jordan admissible algebras. This paper is concerned with algebras which are related to Lie algebras in that they satisfy some of the identities of a Lie algebra and are Lie admissible. Theorem 2 answers a question raised by Albert in (1).

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.

Baer-invariants and extensions relative to a variety

1967 ◽  
Vol 63 (3) ◽  
pp. 569-578 ◽  
Author(s):  
Abraham S.-T. Lue
Keyword(s):  
Commutative Ring ◽  
Lie Algebras ◽  
Associative Algebra ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Definition Of ◽  
The Relationship

This paper examines the relationship between extensions in a variety and general extensions in the category of associative algebras. Our associative algebras are all unitary, over some fixed commutative ring Λ with identity, but while our discussion will be restricted to this category, it is clear that obvious analogues exist for groups, Lie algebras and Jordan algebras. (We use the notion of a bimultiplication of an associative algebra. In (2), Knopfmacher gives the definition of a bimultiplication in any variety of linear algebras.)

scholarly journals Unification Theories: Examples and Applications

Axioms ◽  
2018 ◽  
Vol 7 (4) ◽  
pp. 85 ◽  
Author(s):  
Florin Nichita
Keyword(s):  
Lie Algebras ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Transcendental Numbers

We consider several unification problems in mathematics. We refer to transcendental numbers. Furthermore, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

scholarly journals Unification Theories. Examples and Applications

2018 ◽  
Author(s):  
Florin F. Nichita
Keyword(s):  
Lie Algebras ◽  
Jordan Algebras ◽  
Associative Algebras ◽  
Transcendental Numbers

We consider several unification problems in mathematics. We refer to transcendental numbers. Also, we present some ways to unify the main non-associative algebras (Lie algebras and Jordan algebras) and associative algebras.

On the Levitzki Radical

1974 ◽  
Vol 17 (1) ◽  
pp. 5-10 ◽  
Author(s):  
Tim Anderson
Keyword(s):  
Lie Algebras ◽  
Polynomial Identity ◽  
Important Application ◽  
Jordan Algebras ◽  
Alternative Algebras

The Levitzki radical, which is fundamental in the study of algebras satisfying a polynomial identity, has been shown to exist in the varieties of alternative and Jordan algebras (see Zhevlakov [8], Zwier [9], and Tsai [7]— for an important application of this radical to alternative algebras satisfying a polynomial identity, see Slater [6]). In fact, Hartley [4] even investigated local nilpotence for Lie algebras, though this property can not be radical in the sense of Kurosh-Amitsur [3] for these algebras.

scholarly journals On Jordan Algebras and Some Unification Results

2020 ◽  
Author(s):  
Florin Nichita
Keyword(s):  
Differential Geometry ◽  
Lie Algebras ◽  
Algebraic Structure ◽  
International Workshop ◽  
Jordan Algebras ◽  
Baxter Equation ◽  
Associative Algebras ◽  
Associative Structures

This paper is based on a talk given at the 14-th International Workshop on Differential Geometry and Its Applications, hosted by the Petroleum Gas University from Ploiesti, between July 9-th and July 11-th, 2019. After presenting some historical facts, we will consider some geometry problems related to unification approaches. Jordan algebras and Lie algebras are the main non-associative structures. Attempts to unify non-associative algebras and associative algebras led to UJLA structures. Another algebraic structure which unifies non-associative algebras and associative algebras is the Yang-Baxter equation. We will review topics relared to the Yang-Baxter equation and Yang-Baxter systems, with the goal to unify constructions from Differential Geometry.

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