Homological Transcendence Degree
Rings and Algebras
2007-05-23 v2
Abstract
Let D be a division algebra over a base field k. The homological transcendence degree of D, denoted by Htr D, is defined to be the injective dimension of the enveloping algebra of D. We show that Htr has several useful properties which the classical transcendence degree has. We extend some results of Resco, Rosenberg, Schofield and Stafford, and compute Htr for several classes of division algebras. The main tool for the computation is Van den Bergh's rigid dualizing complex.
Cite
@article{arxiv.math/0412013,
title = {Homological Transcendence Degree},
author = {Amnon Yekutieli and James J. Zhang},
journal= {arXiv preprint arXiv:math/0412013},
year = {2007}
}
Comments
31 pages. Final version, to appear in Proc. London Math. Soc