Morita equivalence for $k$-algebras
| Autor: | Aubert, Anne-Marie, Baum, Paul, Plymen, Roger, Solleveld, Maarten |
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| Rok vydání: | 2017 |
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| Zdroj: | Banach Centre Publications 120 (2020), 245-265 |
| Druh dokumentu: | Working Paper |
| Popis: | We review Morita equivalence for finite type $k$-algebras $A$ and also a weakening of Morita equivalence which we call stratified equivalence. 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 extended affine Weyl groups. Comment: 23 pages. This version is shorter, more readable, has a new title, and supersedes appendix A in arXiv:1505.04361 and arXiv:1211.0180 |
| Databáze: | arXiv |
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