Results 11 to 20 of about 601 (176)
Noncommutative Differential Geometry of Generalized Weyl Algebras [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2016 Elements of noncommutative differential geometry of ${\mathbb Z}$-graded generalized Weyl algebras ${\mathcal A}(p;q)$ over the ring of polynomials in two variables and their zero-degree subalgebras ${\mathcal B}(p;q)$, which themselves are generalized Weyl algebras over the ring of polynomials in one variable, are discussed.
Brzeziński, T., Tomasz Brzezinski
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Noncommutative Geometry in the Framework of Differential Graded Categories [PDF]
, 2010 19 pages.
Snigdhayan Mahanta +3 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
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Comparison between two differential graded algebras in noncommutative geometry [PDF]
Proceedings - Mathematical Sciences, 2019 Starting with a spectral triple one can associate two canonical differential graded algebras (dga) defined by Connes and Fröhlich et al. For the classical spectral triples associated with compact Riemannian spin manifolds both these dgas coincide with the de-Rham dga.
Chakraborty, Partha Sarathi +1 more
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Non-commutative complex differential geometry
Journal of Geometry and Physics, 2013 This paper defines and examines the basic properties of noncommutative analogues of almost complex structures, integrable almost complex structures, holomorphic curvature, cohomology, and holomorphic sheaves. The starting point is a differential structure on a noncommutative algebra defined in terms of a differential graded algebra. This is compared to
Beggs, Edwin, Smith, S. Paul
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Deformation quantization and intrinsic noncommutative differential geometry
, 2023 We provide an intrinsic formulation of the noncommutative differential geometry developed earlier by Chaichian, Tureanu, R. B. Zhang and the second author. This yields geometric definitions of covariant derivatives of noncommutative metrics and curvatures, as well as the noncommutative version of the first and the second Bianchi identities.
Gao, Haoyuan, Zhang, Xiao
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Field Theory on Curved Noncommutative Spacetimes [PDF]
Symmetry, Integrability and Geometry: Methods and Applications, 2010 We study classical scalar field theories on noncommutative curved spacetimes. Following the approach of Wess et al. [Classical Quantum Gravity 22 (2005), 3511 and Classical Quantum Gravity 23 (2006), 1883], we describe noncommutative spacetimes by using (
Alexander Schenkel +1 more
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Some aspects of noncommutative differential geometry
, 1995 We discuss in some generality aspects of noncommutative differential geometry associated with reality conditions and with differential calculi. We then describe the differential calculus based on derivations as generalization of vector fields, and we show its relations with quantum mechanics. Finally we formulate a general theory of connections in this
Michel Dubois-Violette
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Noncommutative differential geometry, and the matrix representations of generalised algebras [PDF]
Journal of Geometry and Physics, 1998 16 pages Latex, No figures.
Gratus, Jonathan
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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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