Titlebook: Elements of Noncommutative Geometry; José M. Gracia-Bondía,Joseph C. Várilly,Héctor Fig Textbook 2001 Springer Science+Business Media New

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Quantum Theorythus a source of noncommutative geometry. Having come so far, it would be a pity not to develop fermion quantum dynamics in external fields, which comes straight from the spin representation. As on many occasions in this book, we set to work here on an enterprise of translation; in this case, to ren

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Kreimer-Connes-Moscovici Algebrason foliations 114, and the ones introduced by Kreimer in connection with perturbative renormalization theory 296. Both types of Hopf algebras were originally found as organizing principles to simplify some computations. This is not unexpected, in view of our discussion at the end of Chapter 1.

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Noncommutative Topology: Vector Bundlesgical partners corresponding to modules over C(.); under suitable conditions, these partners turn out to be the vector bundles over M. The heart of this chapter is thus the Serre-Swan theorem, establishing that the categories of finitely generated projective modules over (.) and the category of vector bundles over . are equivalent.

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Quantum Theoryes straight from the spin representation. As on many occasions in this book, we set to work here on an enterprise of translation; in this case, to render in algebraic terms the quantization of wave equations of the Dirac type. Most of the footwork has already been laid in Section 6.4.

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Christina Rosenlund,Rico Frederik Schou set, specifically the doubly periodic meromorphic functions: Weierstrass opened up a new approach to geometry by studying directly the collection of complex functions that satisfy an algebraic addition theorem, and derived the point set as a consequence 51.