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Noncommutative Jordan C*-algebras
Manuscripta Mathematica, 1982 We introduce noncommutative JB*-algebras which generalize both B*-algebras and JB*-algebras and set up the bases for a representation theory of noncommutative JB*-algebras. To this end we define noncommutative JB*-factors and study the factor representations of a noncommutative JB*-algebra.
Payá, R., Pérez, J., Rodriguez, A.
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Norms and noncommutative Jordan algebras [PDF]
Pacific Journal of Mathematics, 1965 The author defines \(Q\) to be a form on a vector spare \(X\) if \(Q\) is a homogeneous polynomial function on \(X\). For any rational mapping \(F\) from a space \(X_1\) into \(X_2\) let \(\partial F\) denote the differential of \(F\) and \(\partial F\,|_x\), the differential at \(x \in X_1\). Now \(\partial F\,|_x\) is a linear map and \(\partial_u F\,
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On Generalizations of Jacobi–Jordan Algebras
AxiomsIn this paper, we present some generalizations of Jacobi–Jordan algebras. More concretely, we will focus on noncommutative Jacobi–Jordan algebras, Malcev–Jordan algebras, and general Jacobi–Jordan algebras.
Hani Abdelwahab +3 more
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Noncommutative Jordan algebras of characteristic 0 [PDF]
Proceedings of the American Mathematical Society, 1955 That is, A is flexible (a weaker condition than commutativity). If a unity element is adjoined to A in the usual fashion, then a necessary and sufficient condition that (2) be satisfied in the extended algebra is that both (2) and (3) be satisfied in A. We define a noncommutative Jordan algebra A over an arbitrary field F to be an algebra satisfying (1)
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Structure theory for noncommutative Jordan H∗-algebras
Journal of Algebra, 1987 The theory of associative Hilbert algebras as developed in [\textit{W. Ambrose}, Trans. Am. Math. Soc. 57, 364-386 (1945; Zbl 0060.269)] has been extended to various classes of nonassociative algebras, among them Jordan algebras, cf. [\textit{C. Viola Devapakkiam}, Math. Proc. Camb. Philos. Soc. 78, 293-300 (1975; Zbl 0357.17015) and with \textit{P. S.
Mira, JoséAntonio Cuenca +1 more
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The Algebraic and Geometric Classification of Noncommutative Jordan Algebras
Frontiers of MathematicsarXiv admin note: text overlap with arXiv:2406 ...
Abdelwahab, Hani +2 more
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Journal of Algebra, 1995 AbstractIn this paper we study the noncommutative Jordan real division algebras of dimension 8, whose Lie derivation algebra is nontrivial and give an affirmative answer to a question posed by Benkart and Osborn. We characterize also the noncommutative Jordan real division algebras of dimension 8, whose automorphism group is nontrivial.
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Flexible Algebras of Degree Two [PDF]
, 1972 All known examples of simple flexible power-associative algebras of degree two are either commutative or noncommutative Jordan. In this paper we construct an algebra which is partially stable but not commutative and not a noncommutative Jordan algebra ...
Mayne, Joseph H
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Nodal Noncommutative Jordan Algebras [PDF]
Transactions of the American Mathematical Society, 1964 1. A finite-dimensional power-associative algebra ' is said to be nodal [6] if every element of V can be written as a I + z where ai E c 1 is the unity element of W and z is nilpotent and if the set of all nilpotent elements is not a subalgebra of W. In [3; 4], Kokoris has shown that every simple nodal noncommutative Jordan algebra of characteristic p ...
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