Homological transcendence degree Academic Article uri icon

abstract

  • Abstract Let $ D $ be a division algebra over a base field $ k $. The homological transcendence degree of $ D $, denoted by $\text {Htr}\; D $, is defined to be the injective dimension of the algebra $ D\otimes_k D^{\circ} $. We show that $\text {Htr} $ has several useful properties which the classical transcendence degree has. We extend some results of Resco, Rosenberg, Schofield and Stafford, and compute $\text {Htr} $ for several classes of division algebras. The main tool for the computation is Van den Bergh's rigid dualizing complex.

publication date

  • January 1, 2006