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Examples of noncommutative manifolds: complex tori and spherical manifolds
, 2007 We survey some aspects of the theory of noncommutative manifolds focusing on the noncommutative analogs of two-dimensional tori and low-dimensional spheres. We are particularly interested in those aspects of the theory that link the differential geometry
Plazas, Jorge
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Aspects of noncommutative geometry of Bunce–Deddens algebras
Journal of Noncommutative Geometry, 2023 We define and study smooth subalgebras of Bunce–Deddens C^∗ -algebras. We discuss various aspects of noncommutative geometry of Bunce–Deddens algebras including derivations on smooth subalgebras, as well as
Klimek, Slawomir +2 more
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Non-commutative moduli spaces of topological D-branes
, 2005 We give a general construction of extended moduli spaces of topological D-branes as non-commutative algebraic varieties. This shows that noncommutative symplectic geometry in the sense of Kontsevich arises naturally in String ...
Alexandrov +23 more
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AxiomsWe introduce Recognition Geometry (RG), an axiomatic framework in which geometric structure is not assumed a priori but derived. The starting point of the theory is a configuration space together with recognizers that map configurations to observable ...
Jonathan Washburn +2 more
doaj +1 more source
Noncommutative algebraic geometry
Revista Matemática Iberoamericana, 2003 The need for a noncommutative algebraic geometry is apparent in classical invariant and moduli theory. It is, in general, impossible to find commuting parameters parametrizing all orbits of a Lie group acting on a scheme. When one orbit is contained in the closure of another, the orbit space cannot, in a natural way, be given a scheme structure.
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Quantum Frustration as a Protection Mechanism in Non‐Topological Majorana Qubits
Annalen der Physik, Volume 538, Issue 4, April 2026.Quantum frustration is proposed as a robust protection mechanism for non‐topological ‐junction qubit. By leveraging distinct spatial profiles, co‐located Majorana modes couple to independent environments, creating incompatible pointer bases that suppress decoherence.
E. Novais
wiley +1 more source
Structural Properties of The Clifford–Weyl Algebra
MathematicsThe Clifford–Weyl algebra 𝒜q±, as a class of solvable polynomial algebras, combines the anti-commutation relations of Clifford algebras 𝒜q+ with the differential operator structure of Weyl algebras 𝒜q−. It exhibits rich algebraic and geometric properties.
Jia Zhang, Gulshadam Yunus
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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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ZAMM - Journal of Applied Mathematics and Mechanics / Zeitschrift für Angewandte Mathematik und Mechanik, Volume 106, Issue 4, April 2026.ABSTRACT The Lie group SE3$SE\left(3\right)$ of isometric orientation‐preserving transformation is used for modeling multibody systems, robots, and Cosserat continua. The use of these models in numerical simulation and optimization schemes necessitates the exponential map, its right‐trivialized differential (often referred to as the tangent operator ...
Andreas Müller
wiley +1 more source
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