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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.
Elisabete Barreiro +2 more
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Pseudo-Euclidean Jordan Algebras [PDF]
Communications in Algebra, 2015 39 ...
Said Benayadi, Amir Baklouti
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A COORDINATIZATION THEOREM FOR JORDAN ALGEBRAS. [PDF]
Proc Natl Acad Sci U S A, 1962 Throughout this note, the term “algebra” is used for algebra over a field Φ of characteristic ≠2, not necessarily associative or of finite dimensionality. Let D be such an algebra with an identity 1 and an involution d → \( \bar d \). We can form the matrix algebra D n of n × n matrices with entries in D and the usual matrix compositions of addition ...
Jacobson N.
europepmc +5 more sources
Differential calculus on Jordan algebras and Jordan modules [PDF]
Letters in Mathematical Physics, 2018 Having in mind applications to particle physics we develop the differential calculus over Jordan algebras and the theory of connections on Jordan modules. In particular we focus on differential calculus over the exceptional Jordan algebra and provide a complete characterization of the theory of connections for free Jordan modules.
Ludwik Dabrowski +1 more
exaly +4 more sources
Jordan algebras of capacity two. [PDF]
Proc Natl Acad Sci U S A, 1967 Osborn JM.
europepmc +5 more sources
Homotopes of Quasi-Jordan Algebras
Axioms, 2023 The notion of quasi-Jordan algebras was originally proposed by R. Velasquez and R. Fellipe. Later, M. R. Bremner provided a modification called K-B quasi-Jordan algebras; these include all Jordan algebras and all dialgebras, and hence all associative ...
Reem K. Alhefthi +2 more
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Composites and Categories of Euclidean Jordan Algebras [PDF]
Quantum, 2020 We consider possible non-signaling composites of probabilistic models based on euclidean Jordan algebras (EJAs), satisfying some reasonable additional constraints motivated by the desire to construct dagger-compact categories of such models. We show that
Howard Barnum +2 more
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Solutions of Yang–Baxter Equation of Mock-Lie Algebras and Related Rota Baxter Algebras
Computer Sciences & Mathematics Forum, 2023 This paper discusses the relationship between Mock-Lie algebras, Lie algebras, and Jordan algebras. It highlights the importance of the Yang–Baxter equation and symplectic forms in the study of integrable systems, quantum groups, and topological quantum ...
Amir Baklouti
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Generalized Jordan N-Derivations of Unital Algebras with Idempotents
Journal of Mathematics, 2021 Let A be a unital algebra with idempotent e over a 2-torsionfree unital commutative ring ℛ and S:A⟶A be an arbitrary generalized Jordan n-derivation associated with a Jordan n-derivation J.
Xinfeng Liang
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