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引用次数: 0
摘要
摘要定义了k维光滑流形W上一类秩k的向量束的李代数结构,它们与切束TW同构。我们构造了这类向量束的一个令人兴奋的例子。这个例子是基于偏卡普托分数阶导数构造的。我们称这个向量束为分数向量束,用$${\mathscr {F}}^{\nu } {\mathscr {W}}$$ F ν W表示。
A Lie Algebroid Structure for Vector Bundles of Finite Rank Isomorphic to Tangent Bundle of Their Base Space
Abstract We define a Lie algebroid structure for a class of vector bundles of rank k over a k -dimensional smooth manifold W , which are isomorphic to the tangent bundle TW . We construct an exciting example of these types of vector bundles. This example is constructed based on partial Caputo fractional derivatives. We call this vector bundle a fractional vector bundle and denote it by $${\mathscr {F}}^{\nu } {\mathscr {W}}$$ FνW .
期刊介绍:
Journal of Nonlinear Mathematical Physics (JNMP) publishes research papers on fundamental mathematical and computational methods in mathematical physics in the form of Letters, Articles, and Review Articles.
Journal of Nonlinear Mathematical Physics is a mathematical journal devoted to the publication of research papers concerned with the description, solution, and applications of nonlinear problems in physics and mathematics.
The main subjects are:
-Nonlinear Equations of Mathematical Physics-
Quantum Algebras and Integrability-
Discrete Integrable Systems and Discrete Geometry-
Applications of Lie Group Theory and Lie Algebras-
Non-Commutative Geometry-
Super Geometry and Super Integrable System-
Integrability and Nonintegrability, Painleve Analysis-
Inverse Scattering Method-
Geometry of Soliton Equations and Applications of Twistor Theory-
Classical and Quantum Many Body Problems-
Deformation and Geometric Quantization-
Instanton, Monopoles and Gauge Theory-
Differential Geometry and Mathematical Physics