Results 161 to 170 of about 471,891 (193)
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A Jordan Algebra of a Mal’tsev Algebra
Journal of Mathematical Sciences, 2023This study generalizes the Jordan algebra of a Lie algebra and the existing results on the local finite-dimensionality of Lie PI-algebras with an algebraic adjoint representation to Mal'tsev algebras. It illustrates that Jordan algebras of a Mal'tsev algebra inherit nondegeneracy and strong primeness.
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Canadian Journal of Mathematics, 1981
In the theory of Jordan algebras one encounters several definitions of the trace, and it is sometimes unclear whether the different notions are equivalent or not. If we restrict attention to the so–called JB–algebras studied in [2] and their weakly closed analogues JBW–algebras [8], we shall in the present note show that the different concepts are all ...
Pedersen, Gert Kjaergard +1 more
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In the theory of Jordan algebras one encounters several definitions of the trace, and it is sometimes unclear whether the different notions are equivalent or not. If we restrict attention to the so–called JB–algebras studied in [2] and their weakly closed analogues JBW–algebras [8], we shall in the present note show that the different concepts are all ...
Pedersen, Gert Kjaergard +1 more
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INTEGRATION ON JORDAN ALGEBRAS
Mathematics of the USSR-Izvestiya, 1984See the review in Zbl 0516.46044.
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Algebra and Logic, 1988
This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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This work is based on the results and methods of the author's earlier study of Jordan \(A\)-algebras [Algebra Logika 26, No. 6, 731--755 (1987; Zbl 0648.17008)]. The term algebra is used when working over a commutative associative ring with \(1/2\), while the term ring is used when working over the integers.
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Communications in Algebra, 2008 In this article we introduce a new algebraic structure of Jordan type and we show several examples. This new structure, called “quasi-Jordan algebras,” appears in the study of the product x y = 1 2 x y + y x where x y are elements in a dialgebra D ...
Raúl Velasquez
exaly +1 more source
1994
Abstract In this chapter we introduce Jordan algebras and prove their most fundamental properties. Further developments of an algebraic nature will be presented in later chapters, as needed. We restrict ourselves to finite dimensional algebras over the real or complex field and, except in Section 1, assume the existence of an identity ...
Jacques Faraut, Adam Korányi
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Abstract In this chapter we introduce Jordan algebras and prove their most fundamental properties. Further developments of an algebraic nature will be presented in later chapters, as needed. We restrict ourselves to finite dimensional algebras over the real or complex field and, except in Section 1, assume the existence of an identity ...
Jacques Faraut, Adam Korányi
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Jacobi–Jordan-admissible algebras and pre-Jacobi–Jordan algebras
Journal of Algebra and Its ApplicationsThe main purpose of this paper is to study Jacobi–Jordan-admissible algebras and some particular classes like pre-Jacobi–Jordan algebras. First, we provide characterizations of Jacobi–Jordan algebras by means of oxidation process. Then, we discuss Jacobi–Jordan-admissible algebras for which we obtain a surprising characterization as 3-power anti ...
Amir Baklouti +3 more
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Imbedding of Jordan Algebras into Lie Algebras. I
American Journal of Mathematics, 1967For a Jordan algebra \(J\) with identity, the author defines a product on \(L(J) = H\oplus J\oplus J\), where \(H\) is the subring of the endomorphism ring of \(J\) generated by all left multiplications. \(L(J)\) becomes a Lie algebra. Furthermore, \(J\) is such an integral part of L(J) that many properties of \(J\) are also properties of L(J), e.g ...
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On Isometries of Jordan Algebras
Journal of the London Mathematical Society, 1978Wright, J. D. Maitland, Youngson, M. A.
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