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HOMOLOGICAL TRANSCENDENCE DEGREE

Published online by Cambridge University Press:  09 June 2006

AMNON YEKUTIELI  and
JAMES J. ZHANG
AMNON YEKUTIELI
Affiliation:
Department of Mathematics, Ben Gurion University, Be'er Sheva 84105, [email protected]
JAMES J. ZHANG
Affiliation:
Department of Mathematics, Box 354350, University of Washington, Seattle, WA 98195, [email protected]
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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.

Keywords

16A3916K4016E10
Type
Research Article
Information
Proceedings of the London Mathematical Society , Volume 93 , Issue 1 , July 2006 , pp. 105 - 137
Copyright
2006 London Mathematical Society

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