Results 11 to 20 of about 16,964 (172)
Advances in Difference Equations, 2020 Quantum calculus (the calculus without limit) appeared for the first time in fluid mechanics, noncommutative geometry and combinatorics studies. Recently, it has been included into the field of geometric function theory to extend differential operators ...
Rabha W. Ibrahim +2 more
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Connections on central bimodules in noncommutative differential geometry [PDF]
Journal of Geometry and Physics, 1996 We define and study the theory of derivation-based connections on a recently introduced class of bimodules over an algebra which reduces to the category of modules whenever the algebra is commutative. This theory contains, in particular, a noncommutative generalization of linear connections.
Dubois-Violette, Michel +1 more
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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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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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Quantum Riemannian geometry of phase space and nonassociativity
Demonstratio Mathematica, 2017 Noncommutative or ‘quantum’ differential geometry has emerged in recent years as a process for quantizing not only a classical space into a noncommutative algebra (as familiar in quantum mechanics) but also differential forms, bundles and Riemannian ...
Beggs Edwin J., Majid Shahn
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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.
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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 Fr hlich 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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Some special types of determinants in graded skew P BW extensions.
Revista Integración, 2021 In this paper, we prove that the Nakayama automorphism of a graded skew PBW extension over a finitely presented Koszul Auslanderregular algebra has trivial homological determinant.
Héctor Suárez +2 more
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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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Noncommutative scalar fields: Quantum symmetries and braided BV quantization [PDF]
Kragujevac Journal of ScienceIt is strongly believed that the fully consistent quantum gravity theory should lead to a quantum spacetime. The continuous description of spacetime in terms of differential manifolds is no longer adequate at the quantum gravity energies.
Bežanić Milorad +2 more
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