Results 31 to 40 of about 3,742 (131)
The Dual Gromov-Hausdorff Propinquity [PDF]
, 2014 Motivated by the quest for an analogue of the Gromov-Hausdorff distance in noncommutative geometry which is well-behaved with respect to C*-algebraic structures, we propose a complete metric on the class of Leibniz quantum compact metric spaces, named ...
Alfsen +45 more
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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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Reversible skew laurent polynomial rings and deformations of poisson automorphisms [PDF]
, 2009 A skew Laurent polynomial ring S = R[x(+/- 1); alpha] is reversible if it has a reversing automorphism, that is, an automorphism theta of period 2 that transposes x and x(-1) and restricts to an automorphism gamma of R with gamma = gamma(-1).
DAVID A. JORDAN +7 more
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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
wiley +1 more source
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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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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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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Explicit representations of 3-dimensional Sklyanin algebras associated to a point of order 2
, 2017 The representation theory of a 3-dimensional Sklyanin algebra $S$ depends on its (noncommutative projective algebro-) geometric data: an elliptic curve $E$ in $\mathbb{P}^2$, and an automorphism $\sigma$ of $E$ given by translation by a point. Indeed, by
Reich, Daniel J., Walton, Chelsea
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