%0 Journal Article
%T Homological dimensions of smooth and complex analytic quantum tori
%A A. Yu. Pirkovskii
%J Mathematics
%D 2009
%I arXiv
%X 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.
%U http://arxiv.org/abs/0907.0747v1