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- W2981103301 abstract "In this paper, we trace the development of concepts of differential geometry such as a first order differential calculus, an algebra of differential forms and a connection from Euclidean geometry to noncommutative geometry. We begin with basic structures of differential geometry in n-dimensional Euclidean space such as vector field, differential form, connection and then, having explained a general idea of non-commutative geometry, we show how these notions can be developed in the assumption that the algebra of smooth functions on Euclidean space is replaced by its non-commutative analog and the differential graded algebra of differential forms is replaced by a q-differential graded algebra, where q is a primitive Nth root of unity and a differential d of this algebra satisfies the equation dN = 0." @default.
- W2981103301 created "2019-10-25" @default.
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- W2981103301 date "2019-01-01" @default.
- W2981103301 modified "2023-09-27" @default.
- W2981103301 title "Connections in Euclidean and Non-commutative Geometry" @default.
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- W2981103301 doi "https://doi.org/10.1007/978-3-030-23854-4_14" @default.
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