Abstract Happel constructed a fully faithful functor H : D b ( mod Λ ) → mod _ Z T ( Λ ) for a finite dimensional algebra Λ. He also showed that this functor H gives an equivalence precisely when gldim Λ ∞ . Thus if H gives an equivalence, then it provides a canonical tilting object H ( Λ ) of mod Z T ( Λ ) . In this paper we generalize the Happel functor H in the case where T ( Λ ) is replaced with a finitely graded IG-algebra A. We study when this functor is fully faithful or is an equivalence. For this purpose we introduce the notion of homologically well-graded (hwg) IG-algebra, which can be characterized as an algebra posses a homological symmetry which, a posteriori, guarantee that the algebra is IG. We prove that hwg IG-algebras is precisely the class of finitely graded IG-algebras that the Happel functor is fully faithful. We also identify the class that the Happel functor gives an equivalence. As a consequence of our result, we see that if H gives an equivalence, then it provides a canonical tilting object H ( T ) of CM _ Z A . For some special classes of finitely graded IG-algebras, our tilting objects H ( T ) coincide with tilting object constructed in previous works.

中文翻译：

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Happel 函子和同调良好分级的 Iwanaga-Gorenstein 代数

摘要 Happel 为有限维代数Λ 构造了一个完全忠实的函子H : D b ( mod Λ ) → mod _ ZT ( Λ )。他还表明，当 gldim Λ ∞ 时，这个函子 H 给出了一个等价。因此，如果 H 给出等价，则它提供 mod ZT (Λ) 的规范倾斜对象 H (Λ)。在本文中，我们在 T ( Λ ) 被有限分级的 IG 代数 A 替换的情况下推广了 Happel 函子 H。我们研究了这个函子何时是完全忠实的或等价的。为此，我们引入了同调良好分级 (hwg) IG 代数的概念，它可以表征为具有同调对称性的代数，后验保证代数是 IG。我们证明 hwg IG 代数正是 Happel 函子完全忠实的有限分级 IG 代数类。我们还确定了 Happel 函子给出等价的类。作为我们结果的结果，我们看到如果 H 给出等价，那么它提供了 CM_ZA 的规范倾斜对象 H（T）。对于某些特殊类别的有限分级 IG 代数，我们的倾斜对象 H ( T ) 与先前工作中构建的倾斜对象重合。