Results 31 to 40 of about 4,283 (134)
A Natural Basis for Spinor and Vector Fields on the Noncommutative sphere
, 1997 The product of two Heisenberg-Weil algebras contains the Jordan-Schwinger representation of su(2). This Algebra is quotiented by the square-root of the Casimir to produce a non-associative algebra denoted by $\Psi$.
Gratus, Jonathan
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Structure and Representations of Noncommutative Jordan Algebras [PDF]
Transactions of the American Mathematical Society, 1966 The author first proves an analogue of \textit{N. Jacobson}'s coordinatization theorem [Osaka Math. J. 6, 1--71 (1954; Zbl 0059.02902); Proc. Natl. Acad. Sci. USA 48, 1154--1160 (1962; Zbl 0115.02703)] for noncommutative Jordan algebras with \(n\ge 3\) connected orthogonal idempotents which characterizes such algebras as commutative Jordan algebras \(H(
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On Pre-Hilbert Noncommutative Jordan Algebras Satisfying [PDF]
ISRN Algebra, 2012 Let be a real or complex algebra. Assuming that a vector space is endowed with a pre-Hilbert norm satisfying for all . We prove that is finite dimensional in the following cases. (1) is a real weakly alternative algebra without divisors of zero. (2) is a complex powers associative algebra. (3) is a complex flexible algebraic algebra. (4) is a
Mohamed Benslimane, Abdelhadi Moutassim
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A Generalization of Noncommutative Jordan Algebras [PDF]
Proceedings of the American Mathematical Society, 1959 and consider algebras satisfying (1) and (3). In ?1 we show that such algebras of characteristic not 2 or 3 are strictly power-associative, and in ?2 we establish several properties of the submodules A e(X) of these algebras. In the last section we use these results and follow the arguments in [6] to show the existence of an identity element in the ...
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N$N$‐Soliton Matrix mKdV Solutions: Some Special Solutions Revisited
Studies in Applied Mathematics, Volume 154, Issue 6, June 2025.ABSTRACT In this article, a general solution formula is derived for the d×d${\sf d}\times {\sf d}$‐matrix modified Korteweg–de Vries equation. Then, a solution class corresponding to special parameter choices is examined in detail. Roughly, this class can be described as N$N$‐solitons (in the sense of Goncharenko) with common phase matrix. It turns out
Sandra Carillo +2 more
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Journal of the London Mathematical Society, Volume 111, Issue 3, March 2025.Abstract Given an associative C$\mathbb {C}$‐algebra A$A$, we call A$A$ strongly rigid if for any pair of finite subgroups of its automorphism groups G,H$G, H$, such that AG≅AH$A^G\cong A^H$, then G$G$ and H$H$ must be isomorphic. In this paper, we show that a large class of filtered quantizations are strongly rigid.
Akaki Tikaradze
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Light Cone in a Quantum Spacetime
, 2018 Noncommutative spacetimes are a proposed effective description of the low-energy regime of Quantum Gravity. Defining the microcausality relations of a scalar quantum field theory on the $\kappa$-Minkowski noncommutative spacetime allows us to define for ...
Mercati, Flavio, Sergola, Matteo
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On fixed points of self maps of the free ball [PDF]
, 2018 In this paper, we study the structure of the fixed point sets of noncommutative self maps of the free ball. We show that for such a map that fixes the origin the fixed point set on every level is the intersection of the ball with a linear subspace.
Abate +71 more
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Auto‐Bäcklund Transformations for New Matrix First and Second Painlevé Hierarchies
Studies in Applied Mathematics, Volume 154, Issue 1, January 2025.ABSTRACT We define a new doubly extended matrix second Painlevé hierarchy, and in addition a new extended matrix first Painlevé hierarchy. For the former, we present three auto‐Bäcklund transformations (auto‐BTs) that constitute nontrivial extensions to our new hierarchy of previously derived results on the auto‐BTs of a much simpler matrix second ...
Pilar Ruiz Gordoa, Andrew Pickering
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Noncommutative bispectral Darboux transformations
, 2016 We prove a general theorem establishing the bispectrality of noncommutative Darboux transformations. It has a wide range of applications that establish bispectrality of such transformations for differential, difference and q-difference operators with ...
Geiger, Joel +2 more
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