Morita equivalence for $k$-algebras

Volume 120 / 2020

Anne-Marie Aubert, Paul Baum, Roger Plymen, Maarten Solleveld Banach Center Publications 120 (2020), 245-265 MSC: 14A22, 16G30, 20C08, 33D80. DOI: 10.4064/bc120-16

Abstract

We review Morita equivalence for finite type $k$-algebras $A$ and also a weakening of Morita equivalence which we call \lt em \gt stratified equivalence \lt /em \gt . The spectrum of $A$ is the set of equivalence classes of irreducible $A$-modules. For any finite type $k$-algebra $A$, the spectrum of $A$ is in bijection with the set of primitive ideals of $A$. The stratified equivalence relation preserves the spectrum of $A$ and also preserves the periodic cyclic homology of $A$. However, the stratified 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 stratified equivalence is provided by affine Hecke algebras associated to affine Weyl groups.

Authors

  • Anne-Marie AubertCNRS
    Sorbonne Université
    Université Paris Diderot
    Institut de Mathématiques de Jussieu
    Paris Rive Gauche
    IMJ-PRG
    F-75005 Paris, France
    ORCID: 0000-0002-9613-9140
    e-mail
  • Paul BaumMathematics Department
    Pennsylvania State University
    University Park, PA 16802, USA
    e-mail
  • Roger PlymenSchool of Mathematics
    Alan Turing Building
    Manchester University
    Manchester M13 9PL, UK
    ORCID: 0000-0002-2071-6925
    e-mail
  • Maarten SolleveldIMAPP
    Radboud Universiteit Nijmegen
    Heyendaalseweg 135
    6525AJ Nijmegen, the Netherlands
    ORCID: 0000-0001-6516-6739
    e-mail

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