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Noncommutative topology and Jordan operator algebras [PDF]
Mathematische Nachrichten, 2018 AbstractJordan operator algebras are norm‐closed spaces of operators on a Hilbert space with for all . We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan operator algebras. We show that Jordan operator algebras present perhaps the most general setting for a “full” noncommutative ...
Blecher, David P., Neal, Matthew
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Noncommutative jordan algebras with commutators satisfying an alternativity condition. [PDF]
Proc Natl Acad Sci U S A, 1970 The theorems of this paper show that the main results in the structure and representation theory of Jordan algebras and of alternative algebras are valid for a larger class of algebras defined by simple identities which obviously hold in the Jordan and alternative cass. A new unification of the Jordan and associative theories is also achieved.
Block RE.
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On a class of noncommutative Jordan algebras. [PDF]
Proc Natl Acad Sci U S A, 1966 McCrimmon, K., Schafer, R. D.
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Noncommutative matrix Jordan algebras [PDF]
Transactions of the American Mathematical Society, 1992 We consider noncommutative degree two Jordan algebras J \mathcal {J} of two by two matrices whose off diagonal entries are from an anticommutative algebra S \mathcal {S} . We give generators and relations for the automorphism group of J \mathcal {J} and determine ...
Brown, Robert B., Hopkins, Nora C.
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The standard model, the Pati–Salam model, and ‘Jordan geometry’
New Journal of Physics, 2020 We argue that the ordinary commutative and associative algebra of spacetime coordinates (familiar from general relativity) should perhaps be replaced, not by a noncommutative algebra (as in noncommutative geometry), but rather by a Jordan algebra ...
Latham Boyle, Shane Farnsworth
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Primitive Noncommutative Jordan Algebras with Nonzero Socle [PDF]
Proceedings of the American Mathematical Society, 1986 Let A A be a nondegenerate noncommutative Jordan algebra over a field K K of characteristic ≠ 2 \ne 2 . Defining the socle S ( A ) S(A) of A A to be the socle of the plus algebra A +
Fernández López, Antonio +1 more
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A characterization of nilpotent nonassociative algebras by invertible Leibniz-derivations [PDF]
, 2016 Moens proved that a finite-dimensional Lie algebra over field of characteristic zero is nilpotent if and only if it has an invertible Leibniz-derivation.
Kaygorodov, Ivan, Popov, Yury
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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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Some nodal noncommutative Jordan algebras [PDF]
Proceedings of the American Mathematical Society, 1958 2. S. Lefschetz, Algebraic geometry, Princeton, 1953. 3. H. Levi, On the structure of differential polynomials and on their theory of ideals, Trans. Amer. Math. Soc. vol. 51 (1942) pp. 532-568. 4. J. F. Ritt, Differential algebra, Amer. Math. Soc. Colloquium Publications, vol. 33, New York, 1950. 5. A.
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