Homological dimensions of smooth and complex analytic quantum tori

Details Homological dimensions of smooth and complex analytic quantum tori Homological dimensions of smooth and complex analytic quantum tori

2009-07-04

arxiv.org/abs/0907.0747v1

Mathematics

Functional Analysis

14 pages

Scientific paper

We survey some results on homological dimensions of the algebraic, complex analytic, and smooth quantum tori. Our main theorem states, in particular, that the smooth and the complex analytic quantum n-tori have global dimension n. This contrasts with the result of McConnell and Pettit (1988) who proved that, in the generic case, the algebraic quantum n-torus has global dimension 1. In this connection we also formulate some general theorems on homological dimensions of nuclear Fr\'echet algebras.

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