Homological Transcendence Degree

2004/12/01 by Amnon Yekutieli, Yekutieli, Amnon, James J. Zhang +1 · 1 citation
Mathematics · #16A39 #16E10 #16K40 #16W50 #FOS: Mathematics #Rings and Algebras (math.RA) #math.RA #msc:16A39 #msc:16E10 #msc:16K40 #msc:16W50

paper · pdf · doi:10.48550/arxiv.math/0412013

31 pages. Final version, to appear in Proc. London Math. Soc

arxiv created 2005/08/06 · arxiv updated 2009/12/01

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.

Cited by

• Galois Rings, Coulomb branches and the Gelfand-Kirillov Conjecture

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• Transcendence Degree of Division Algebras
• The Transcendence Degree over a Ring
• Fields of definition for division algebras
• Commutative subalgebras of U(\mathfrak q) of maximal transcendence degree
• Gelfand-Kirillov dimension of commutative subalgebras of simple infinite dimensional algebras and their quotient division algebras