Leibniz Rules and Reality Conditions

Details Leibniz Rules and Reality Conditions Leibniz Rules and Reality Conditions

1998-06-12

arxiv.org/abs/math/9806071v1

Mathematics

Quantum Algebra

13 pages, LaTeX2e

Scientific paper

An analysis is made of reality conditions within the context of noncommutative geometry. We show that if a covariant derivative satisfies a given left Leibniz rule then a right Leibniz rule is equivalent to the reality condition. We show also that the matrix which determines the reality condition must satisfy the Yang-Baxter condition if the extension of the covariant derivative to tensor products is to satisfy the reality condition. This is equivalent to the braid condition for the matrix which determines the right Leibniz rule.

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