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PRIME SPECTRA OF QUANTIZED COORDINATE RINGS K. R. Goodearl
 

Summary: PRIME SPECTRA OF QUANTIZED COORDINATE RINGS
K. R. Goodearl
This paper is partly a report on current knowledge concerning the struc­
ture of (generic) quantized coordinate rings and their prime spectra, and
partly propaganda in support of the conjecture that since these algebras
share many common properties, there must be a common basis on which to
treat them. The first part of the paper is expository. We survey a num­
ber of classes of quantized coordinate rings, as well as some related algebras
that share common properties, and we record some of the basic properties
known to occur for many of these algebras, culminating in stratifications of
the prime spectra by the actions of tori of automorphisms. As our main
interest is in the generic case, we assume various parameters are not roots
of unity whenever convenient. In the second part of the paper, which is
based on [20], we offer some support for the conjecture above, in the form of
an axiomatic basis for the observed stratifications and their properties. At
present, the existence of a suitable supply of normal elements is taken as one
of the axioms; the search for better axioms that yield such normal elements
is left as an open problem.
I. Quantized Coordinate Rings and Related Algebras
This part of the paper is an expository account of the prime ideal structure

  

Source: Akhmedov, Azer - Department of Mathematics, University of California at Santa Barbara

 

Collections: Mathematics