论文标题
解决二元性和对同源不变的应用
Resolving dualities and applications to homological invariants
论文作者
论文摘要
在Artin代数上解决有限生成的模块的子类别的二元性被描述为二元性相对于Wakamatsu倾斜双模型。通过限制这些双重性来解决有限生成的模块的子类别，该模块具有有限的投影或Gorenstein-Prokentive尺寸，Miyashita的二元性以及Huisgen-Zimmermann在倾斜模块上的对应关系以及其Gorenstein版本。应用包括构建有限生成的Gorenstein-Prokentive模块的衍生类别的三角等效，并显示了有限生成的Gorenstein-Projective模块的较高代数$ k $ grou和半衍生的林格尔代数的不变性。
Dualities of resolving subcategories of finitely generated modules over Artin algebras are characterized as dualities with respect to Wakamatsu tilting bimodules. By restriction of these dualities to resolving subcategories of finitely generated modules with finite projective or Gorenstein-projective dimensions, Miyashita's duality and Huisgen-Zimmermann's correspondence on tilting modules as well as their Gorenstein version are obtained. Applications include constructing triangle equivalences of derived categories of finitely generated Gorenstein-projective modules and showing the invariance of higher algebraic $K$-groups and semi-derived Ringel-Hall algebras of finitely generated Gorenstein-projective modules under tilting.
