Aubert, AnneMarie and Baum, Paul and Plymen, Roger and Solleveld, Maarten (2017) On the spectra of finite type algebras. [MIMS Preprint]
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Abstract
Let X be a complex affine variety and k its coordinate algebra. This paper will review Morita equivalence for kalgebras and will then review, for finite type kalgebras, a weakening of Morita equivalence called spectral equivalence. The spectrum of A is, by definition, the set of equivalence classes of irreducible Amodules. For any finite type kalgebra A, the spectrum of A is in bijection with the set of primitive ideals of A. The spectral equivalence relation preserves the spectrum of A and also preserves the periodic cyclic homology of A. However, the spectral equivalence relation permits a tearing apart of strata in the primitive ideal space which is not allowed by Morita equivalence. A key example illustrating the distinction between Morita equivalence and spectral equivalence relation is provided by affine Hecke algebras associated to affine Weyl groups. We also review the role of spectral equivalence in the ABPS conjecture.
Item Type:  MIMS Preprint 

Uncontrolled Keywords:  Spectrum, Morita equivalence, spectral equivalence 
Subjects:  MSC 2010, the AMS's Mathematics Subject Classification > 14 Algebraic geometry MSC 2010, the AMS's Mathematics Subject Classification > 16 Associative rings and algebras MSC 2010, the AMS's Mathematics Subject Classification > 22 Topological groups, Lie groups 
Depositing User:  Professor Roger Plymen 
Date Deposited:  27 Feb 2017 
Last Modified:  20 Oct 2017 14:13 
URI:  http://eprints.maths.manchester.ac.uk/id/eprint/2534 
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On the spectra of finite type algebras. (deposited 14 Feb 2017)
 On the spectra of finite type algebras. (deposited 27 Feb 2017) [Currently Displayed]
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