We study certain special tilting and cotilting modules for an algebra with positive dominant dimension, each of which is generated or cogenerated (and usually both) by projective-injectives. These modules have various interesting properties, for example, that their endomorphism algebras always have global dimension less than or equal to that of the original algebra. We characterise minimal d-Auslander–Gorenstein algebras and d-Auslander algebras via the property that these special tilting and cotilting modules coincide. By the Morita–Tachikawa correspondence, any algebra of dominant dimension at least 2 may be expressed (essentially uniquely) as the endomorphism algebra of a generator-cogenerator for another algebra, and we also study our special tilting and cotilting modules from this point of view, via the theory of recollements and intermediate extension functors.

中文翻译：

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具有正主维度的代数的特殊倾斜模块

我们研究了具有正主导维数的代数的某些特殊倾斜和共倾斜模块，其中每个模块都是由射影-内射生成或共同生成的（通常两者兼而有之）。这些模块具有各种有趣的特性，例如，它们的自同态代数的全局维数总是小于或等于原始代数的全局维数。我们表征最小d-Auslander-Gorenstein 代数和d-Auslander 代数通过这些特殊的倾斜和倾斜模块重合的属性。通过 Morita-Tachikawa 对应，任何主维数至少为 2 的代数都可以（本质上唯一地）表示为另一个代数的生成 - 共生子的自同态代数，我们也从这个角度研究了我们的特殊倾斜和倾斜模块，通过回忆理论和中间扩展函子。