Lectures on Differential Geometry of Modules and Rings

Details Lectures on Differential Geometry of Modules and Rings Lectures on Differential Geometry of Modules and Rings

2009-10-08

arxiv.org/abs/0910.1515v2

Physics

Mathematical Physics

137 pages

Scientific paper

Generalizing differential geometry of smooth vector bundles formulated in algebraic terms of the ring of smooth functions, its derivations and the Koszul connection, one can define differential operators, differential calculus and connections on modules over arbitrary commutative, graded commutative and noncommutative rings. For instance, this is the case of quantum theory, SUSY theory and noncommutative geometry, respectively. The relevant material on this subject is summarized.

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