A block extension of categorical results in the Green correspondence context
| Autor: | Morton E. Harris |
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| Rok vydání: | 2014 |
| Předmět: | |
| Zdroj: | Journal of Group Theory. 17:1117-1131 |
| ISSN: | 1435-4446 1433-5883 |
| DOI: | 10.1515/jgth-2014-0021 |
| Popis: | In [J. Pure Appl. Algebra 2 (1972), 371–393, Theorem 4.1], J. A. Green shows that the Green Correspondence in Finite Group Modular Representation Theory is a consequence of an equivalence between two quotient categories of appropriate subcategories in the Green Correspondence context. In [Adv. Math. 104 (1994), 297–314, Theorems 3.5, 3.6 and 3.7], M. Auslander and M. Kleiner prove a similar result. M. Linckelmann suggested that the quotient categories in these results are the same. Utilizing extensions of [The Representation Theory of Finite Groups, North-Holland, Amsterdam, 1982, III, Theorem 7.8] or [Representations of Finite Groups, Academic Press, San Diego, 1988, Chapter 5, Corollary 3.11], we extend these results to blocks of finite groups. In order to state and prove our results and to remain relatively self-contained, we follow the procedures of [Adv. Math. 104 (1994), 297–314] in the Green Correspondent context. This is presented in Section 1. In Section 2 we present our main results. In Section 3 we give a very short proof of a theorem of H. Fitting for 𝒪-algebras that is essential in the proof of basic results of J. A. Green, [J. Pure Appl. Algebra 2 (1972), 371–393, Lemma 3.9 and Theorem 3.10]. |
| Databáze: | OpenAIRE |
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