Quantum Groups and Non-commutative Differential Geometry

Yu. I. Manin
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Yu. I. Manin: Steklov Math. Institute

A chapter in Mathematical Physics X, 1992, pp 113-122 from Springer

Abstract: Abstract Recently it became common to identify the notion of a quantum group with that of a Hopf algebra. However, this does not quite agree with the experience gained in classical group theory. In fact, classically, Hopf algebras arise in the following framework. One starts with a category S of “spaces” (finite sets, schemes, differential manifolds, topological spaces ...) and a linear functor ℱ on it, covariant or contravariant. The functor must satisfy certain formal properties, in particular, transform direct products into tensor products. The values of this functor upon group objects in S will then be Hopf algebras, commutative in the contravariant case, cocommutative in the covariant case.

Keywords: Hopf Algebra; Quantum Group; Quantum Space; Elementary Extension; Plenary Lecture (search for similar items in EconPapers)
Date: 1992
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DOI: 10.1007/978-3-642-77303-7_9

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