Homological Transcendence Degree
By Amnon Yekutieli, James J. Zhang. 2004
62 citations recorded by the source corpus.
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 algebra D ⊗ k 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. 2000 Mathematics Subject Classification 16A39, 16K40, 16E10.
Subfields: Geometry and Topology, Mathematical Physics
View Paper: https://www.semanticscholar.org/paper/f0e54d79579fafacf6e0ea818ca0bd632ef58a2d
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In Geometry and Topology
- Amnon Yekutieli
- James J. Zhang
- James Kuzmanovich
- E. Kirkman
- Masaki Kashiwara
- Michel van den Bergh
- Andrei Căldăraru
- Yukinobu Toda
In Mathematical Physics
- James J. Zhang
- Amnon Yekutieli
- James Kuzmanovich
- E. Kirkman
- Masaki Kashiwara
- Andrei Căldăraru
- Michel van den Bergh
- Yukinobu Toda
Citations in the corpus
- Derived Categories (2016, background): “One application of the rigid localization morphism is in the concept of homological transcendence degree [185] – the ring A is an integral domain which has a rigid dualizing complex (say because of the existence of a good filtration on it), and D = A′ is the division ring of fractions of A.”
- Shephard–Todd–Chevalley Theorem for Skew Polynomial Rings (2008, methodology): “Proof. By induction we may assume d = 2. Then we use the proof of [ YZ , Proposition 4.5(a)].”