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Simple-minded systems in stable module categories
澳门新葡8455最新网站:2014年03月11日 00:00 点击数:

报告人:刘玉明

报告地点:澳门新葡8455最新网站104室

报告澳门新葡8455最新网站:2014年03月14日星期五14:00-15:00

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报告摘要:

Given an artin algebra A, we denote by mod(A), D^b(A), and stmod(A) the category of finitely generated (left) A-modules, the derived category of mod(A) and the stable category of mod(A). By classical Morita theory, projective objects control equivalences of module categories. The role of projective modules can in derived categories be taken over by appropriate generalisations such as tilting complexes, which still control equivalences of such categories. In stable categories, no substitutes of projective objects are known and stable equivalences are, in general, not known to be controlled by particular objects. It is not even known whether equivalences of stable module categories preserve the number of non-projective simple modules; the Auslander-Reiten conjecture - which appears to be wide open - predicts a positive answer to this question. The simple-minded systems can be seen as “simgenerators” of the stable module category mod A, comparing with progenerators of the module category mod A. In this talk, I will introduce some problems on simple-minded systems and give some applications of simple-minded system theory on stable equivalences. The contents are based on joint work with Steffen Koenig and Aaron Chan.

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