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Noncommutative Differential Calculus: Quantum Groups, Stochastic Processes, and the Antibracket

Aristophanes Dimakis, Folkert Mueller-Hoissen

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Abstract

We explore a differential calculus on the algebra of C∞-functions on a manifold. The former is ‘noncommutative’ in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. A similar differential calculus on a superspace is shown to be related to the Batalin-Vilkovisky antifield formalism.

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We explore a differential calculus on the algebra of C∞-functions on a manifold. The former is ‘noncommutative’ in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. A similar differential calculus on a superspace is shown to be related to the Batalin-Vilkovisky antifield formalism.

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Available abstract

We explore a differential calculus on the algebra of C∞-functions on a manifold. The former is ‘noncommutative’ in the sense that functions and differentials do not commute, in general. Relations with bicovariant differential calculus on certain quantum groups and stochastic calculus are discussed. A similar differential calculus on a superspace is shown to be related to the Batalin-Vilkovisky antifield formalism.

Key concepts: Differential calculus, Quantum differential calculus, Noncommutative geometry, Time-scale calculus, Mathematics, Calculus (dental), Pure mathematics, Formalism (music)

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