余挠三元组的应用
Applications of cotorsion triples
摘要：
本文研究了由余挠三元组产生的模型范畴的同伦范畴，以及相应的稳定范畴之间的等价关系。我们刻画了余挠三元组的同调维数。然后将余挠三元组提升到复形，并通过模型范畴的Quillen等价性得到复形同伦范畴的等价性。最后，我们指定Gorenstein余挠三元组$(\mathcal{GP}, \mathcal{W}, \mathcal{GI})$。利用Quillen等价，证明了左Gorenstein环存在等价$\mathrm{K}(\mathcal{GP})\simeq \mathrm{K}(\mathcal{GI})$，它限制于等价$\mathrm{K}(\mathcal{P})\simeq \mathrm{K}(\mathcal{I})$（与[J. Algebra，2010，324：2718-2731]比较），并给出了Gorenstein整体维数的Bennis和Mahdou等式的新证明.
英文摘要：
We study homotopy categories of model categories arising from a cotorsion triple, and the equivalences between corresponding stable categories. We characterize homological dimensions with respect to a cotorsion triple. Then, we lift cotorsion triple to complexes, and get the equivalence of homotopy categories of complexes via Quillen equivalence of model categories. Finally, we specify to Gorenstein cotorsion triple $(\mathcal{GP}, \mathcal{W}, \mathcal{GI})$. By Quillen equivalence, it is shown that for a left-Gorenstein ring, there is an equivalence $\mathrm{K}(\mathcal{GP})\simeq \mathrm{K}(\mathcal{GI})$, which restricts to an equivalence $\mathrm{K}(\mathcal{P})\simeq \mathrm{K}(\mathcal{I})$ (compare to [J. Algebra, 2010, 324:2718-2731]); a new proof for Bennis and Mahdou's equality of Gorenstein global dimension is also given.
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