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Specifying the Auslander–Reiten translation for
complexes of moduleslastyear
期刊名称: Forum Mathematicum
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作者: Shokrollah Salarian,Razieh Vahed
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tablets年份: 2016年
offon期号: 第2期
click click click关键词: Auslander–Reiten quences;maximal Cohen–Macaulay modules;adjoin pair;homotopy category;18G35;18E30;16G50;16G70
anyone摘要:We describe explicitly the Auslander–Reiten translation in the category of bounded complexes of finitely generated maximal Cohen–Macaulay modules,
b(CMR), over a commutative local Cohen–Macaulay ringRwith a canonical module ω. Then the Auslan
der–Reiten formula is generalized for complexes in b(CMR) and we prove the existence theorem of Auslander–Reiten quences. As an application of our results, we investigate the existence of Auslander–Reiten triangles in the category of perfect complexes as a full triangulated subcategory of b(modR).
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