April 13, 2005
Amnon Yekutieli
Title: Homological Transcendence Degree
Let D be a finitely generated division algebra over a field K. In
this talk I will present a new invariant of D called the homological
transcendence degree. As the name suggests the definition involves
homological algebra; but it is a very easy definition. If D is
commutative
(i.e. a field extension of K) then this number coincides with the
classical transcendence degree. For noncommutative rings there are a
couple of older definitions (e.g. the Gelfand-Kirillov tr. deg.), which
are very hard to compute. The main advantage of our new definition is
that we can compute it in many important cases, and prove some
properties
analogous the to commutative case. The key technical tool is Van den
Bergh's rigid dualizing complex. (Joint work with J. Zhang.)
Eprint: math.RA/0412013 at http://arxiv.org.
