Results 31 to 40 of about 16,979 (167)
Noncommutative spectral geometry of Riemannian foliations
, 1997 We construct spectral triples in a sense of noncommutative differential geometry, associated with a Riemannian foliation on a compact manifold, and describe its dimension spectrum.Comment: LaTeX 2.09, 33 ...
Kordyukov, Yuri A.
core +2 more sources
AN INTRODUCTION TO NONCOMMUTATIVE DIFFERENTIAL GEOMETRY ON QUANTUM GROUPS [PDF]
International Journal of Modern Physics A, 1993 We give a pedagogical introduction to the differential calculus on quantum groups by stressing at all stages the connection with the classical case (q→1 limit). The Lie derivative and the contraction operator on forms and tensor fields are found. A new, explicit form of the Cartan-Maurer equations is presented.
Aschieri, Paolo, Castellani, Leonardo
openaire +3 more sources
Noncommutative polygonal cluster algebras
Journal of the London Mathematical Society, Volume 113, Issue 4, April 2026.Abstract We define a new family of noncommutative generalizations of cluster algebras called polygonal cluster algebras. These algebras generalize the noncommutative surfaces of Berenstein–Retakh, and are inspired by the emerging theory of Θ$\Theta$‐positivity for the groups Spin(p,q)$\mathrm{Spin}(p,q)$.
Zachary Greenberg +3 more
wiley +1 more source
Invariant noncommutative connections
, 2004 In this paper we classify invariant noncommutative connections in the framework of the algebra of endomorphisms of a complex vector bundle. It has been proven previously that this noncommutative algebra generalizes in a natural way the ordinary geometry ...
Masson, Thierry, Serie, Emmanuel
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Mathematika, Volume 72, Issue 2, April 2026.Abstract In this paper, we study traces of Hecke operators on Drinfeld modular forms of level 1 in the case A=Fq[T]$A = \mathbb {F}_q[T]$. We deduce closed‐form expressions for traces of Hecke operators corresponding to primes of degree at most 2 and provide algorithms for primes of higher degree.
Sjoerd de Vries
wiley +1 more source
Noncommutative Geometry and Gauge Theory on Fuzzy Sphere [PDF]
, 2000 The differential algebra on the fuzzy sphere is constructed by applying Connes' scheme. The U(1) gauge theory on the fuzzy sphere based on this differential algebra is defined.
Carow-Watamura, Ursula +1 more
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Negativity‐preserving transforms of tuples of symmetric matrices
Proceedings of the London Mathematical Society, Volume 132, Issue 4, April 2026.Abstract Compared to the entrywise transforms which preserve positive semidefiniteness, those leaving invariant the inertia of symmetric matrices reveal a surprising rigidity. We first obtain the classification of negativity preservers by combining recent advances in matrix analysis with some novel arguments relying on well‐chosen test matrices, Sidon ...
Alexander Belton +3 more
wiley +1 more source
Braided Cyclic Cocycles and Non-Associative Geometry
, 2004 We use monoidal category methods to study the noncommutative geometry of nonassociative algebras obtained by a Drinfeld-type cochain twist. These are the so-called quasialgebras and include the octonions as braided-commutative but nonassociative ...
Albuquerque H. +6 more
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31Lectures on Noncommutative Geometry
Acta Polytechnica, 2008 We present a short overview of noncommutative geometry. Starting with C* algebras and noncommutative differential forms we pass to K-theory, K-homology and cyclic (co)homology, and we finish with the notion of spectral triples and the spectral action.
A. Sitarz
doaj
Metric perturbations in noncommutative gravity
Journal of High Energy PhysicsWe use the framework of Hopf algebra and noncommutative differential geometry to build a noncommutative (NC) theory of gravity in a bottom-up approach.
Nikola Herceg +3 more
doaj +1 more source