On the speciality of Jordan algebras and subquotients of Lie algebras
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DOI: 10.1016/j.jalgebra.2020.07.013
Abstract: Abstract In [7] Jordan algebras were attached to ad-nilpotent elements of index less than or equal to three of Lie algebras. In this paper we study conditions on the own structure of the Lie algebras… read more here.
Keywords: lie algebras; speciality jordan; algebras subquotients; jordan algebras ... See more keywords
Weak majorization, doubly substochastic maps, and some related inequalities in Euclidean Jordan algebras
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DOI: 10.1016/j.laa.2020.03.028
Abstract: Abstract In this paper, we extend the notion of weak majorization and doubly substochastic maps, and the Hardy-Littlewood-Polya theorem on majorization to Euclidean Jordan algebras. We also provide a characterization of doubly substochastic maps on… read more here.
Keywords: doubly substochastic; euclidean jordan; weak majorization; jordan algebras ... See more keywords
On vertex operator algebras associated to Jordan algebras of Hermitian type
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DOI: 10.1080/00927872.2019.1646267
Abstract: Abstract In this paper, we construct a family of vertex operator algebras parameterized by a non-zero complex number r, whose Griess algebras V2 are isomorphic to Hermitian Jordan algebras of type C and A with… read more here.
Keywords: vertex; operator algebras; vertex operator; jordan algebras ... See more keywords
Evaluations of multilinear polynomials on low rank Jordan algebras
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DOI: 10.1080/00927872.2021.2021221
Abstract: In this paper we prove the generalized Kaplansky conjecture for Jordan algebras of the type Jn, in particular for self-adjoint 2×2 matrices over R, over C, H and O. In fact, we prove that the… read more here.
Keywords: multilinear polynomials; polynomials low; jordan; evaluations multilinear ... See more keywords
On cohomology and deformations of Jacobi-Jordan algebras
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DOI: 10.1080/00927872.2023.2215872
Abstract: In this paper we study cohomology and deformations of Jacobi-Jordan algebras. We develop their formal deformation theory. In particular, we introduce a method to construct a versal deformation for a given Jacobi-Jordan algebra, which can… read more here.
Keywords: jordan; deformations jacobi; jordan algebras; jacobi jordan ... See more keywords
A class of non-associative Nilpotent Jordan algebras
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DOI: 10.1142/s021949882150002x
Abstract: The paper is devoted to study nilpotent Jordan algebras ???? satisfying that ????/Ann(???? ) is non-associative. We show that such algebras exist iff dim ???? ≥ 6 and dim(????/Ann(???? )) ≥ 5. Also we classify,… read more here.
Keywords: class non; non associative; jordan algebras; nilpotent jordan ... See more keywords
Scattering in Algebraic Approach to Quantum Theory—Jordan Algebras
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DOI: 10.3390/universe9040173
Abstract: Using the geometric approach, we formulate a quantum theory in terms of Jordan algebras. We analyze the notion of a (quasi)particle (=elementary excitation of translation-invariant stationary state) and the scattering of (quasi)particles in this framework. read more here.
Keywords: approach; jordan algebras; quantum theory; scattering algebraic ... See more keywords