Title: Homological Transcendence Degree
Authors: Amnon Yekutieli and James J. Zhang
Publication status: Proc. London Math. Soc. 2006 93 no. 1, 105-137

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.

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updated 13 June 2005