Results 1 to 10 of about 3,743 (118)
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.
europepmc +7 more sources
On a class of noncommutative Jordan algebras. [PDF]
Proc Natl Acad Sci U S A, 1966 McCrimmon, K., Schafer, R. D.
europepmc +5 more sources
Noncommutative topology and Jordan operator algebras [PDF]
Mathematische Nachrichten, 2018 Jordan operator algebras are norm-closed spaces of operators on a Hilbert space with $a^2 \in A$ for all $a \in A$. We study noncommutative topology, noncommutative peak sets and peak interpolation, and hereditary subalgebras of Jordan operator algebras.
Blecher, David P., Neal, Matthew
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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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Derived categories of hearts on Kuznetsov components
Journal of the London Mathematical Society, Volume 108, Issue 6, Page 2146-2174, December 2023., 2023 Abstract We prove a general criterion that guarantees that an admissible subcategory K$\mathcal {K}$ of the derived category of an abelian category is equivalent to the bounded derived category of the heart of a bounded t‐structure. As a consequence, we show that K$\mathcal {K}$ has a strongly unique dg enhancement, applying the recent results of ...
Chunyi Li, Laura Pertusi, Xiaolei Zhao
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Algebraic Techniques for Canonical Forms and Applications in Split Quaternionic Mechanics
Journal of Mathematics, Volume 2023, Issue 1, 2023., 2023 The algebra of split quaternions is a recently increasing topic in the study of theory and numerical computation in split quaternionic mechanics. This paper, by means of a real representation of a split quaternion matrix, studies the problem of canonical forms of a split quaternion matrix and derives algebraic techniques for finding the canonical forms
Tongsong Jiang +5 more
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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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Journal of Mathematics, Volume 2021, Issue 1, 2021., 2021 In this paper, we give an extended quaternion as a matrix form involving complex components. We introduce a semicommutative subalgebra ℂ(ℂ2) of the complex matrix algebra M(4, ℂ). We exhibit regular functions defined on a domain in ℂ4 but taking values in ℂ(ℂ2).
Ji Eun Kim, V. Ravichandran
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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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