Homological Transcendence Degree
Amnon Yekutieli, James J. Zhang
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.
Create a lesson
Related papers
On Jordan nilpotency of index n in group rings
Osnel B. Cristo, Mariana G. Cornelissen, Rodrigo L. Rodrigues
High-Degree Restricted Cohomology for K(3;1)(1) in Characteristics Five and Seven
Chao Ma
Identities of Representation of Lie subalgebras of the first Weyl algebra
Vyacheslav Futorny, Plamen Koshlukov, João Fernando Schwarz
Homology and Topology of Partially Ordered Fields
Hanzhen Bao
Hopf algebra polynomial identities in the Sweedler algebra
Alexey Gordienko, Maria Morozova
Resolvent comparison for Hermitian block matrices and Kelmans transformations
Xianhao Meng, Zhijun Xu, Zhiyuan Zhang