關(guān)于n-平移代數(shù)和n-阿貝爾范疇的研究
發(fā)布時間：2019-07-02 20:50
【摘要】：代數(shù)表示論高維理論是Iyama等人推廣經(jīng)典Auslander-Reiten理論,引入n-Auslander代數(shù)[63], n-Auslander-Reiten平移函子[64]等建立發(fā)展起來的.作為平移代數(shù)的推廣,郭引入了n-平移代數(shù),并揭示了n-平移代數(shù)與高維表示理論的內(nèi)在聯(lián)系[56].本文主要討論兩個方面的問題：一是研究(n+1)-表示有限的n-Auslander代數(shù)(更一般的,n-預(yù)平移立方代數(shù))及其Koszul對偶的平移性、周期性、幾乎Koszul性和n-APR傾斜性等性質(zhì)；二是利用n-阿貝爾范疇刻畫n-Auslander代數(shù).具體組織如下：我們首先研究n-平移代數(shù),第三章我們研究n-立方代數(shù),計算它們與扭平凡擴張代數(shù)的單模投射分解.第四章我們從(n+1)-表示有限的n-Auslander代數(shù)出發(fā)引入(穩(wěn)定)n-金字塔代數(shù),并研究它們及其Kosuzl對偶的Koszul性、周期性、平移性.第五章我們研究Υ[n]n-mutation,對于整體維數(shù)小于等于n的Koszul代數(shù),如果其Kosuzl對偶為允許(n-1)-平移代數(shù),則其n-APR傾斜為原代數(shù)的T[n]-mutation.在第六章,我們研究高維Auslander對應(yīng).作為Iyama-Beligiannis的n-Auslander對應(yīng)的推廣,我們利用n-阿貝爾范疇給出n-Auslander 對應(yīng),從而給出一個利用n-阿貝爾范疇的n-Auslander范疇的刻畫.并在此基礎(chǔ)上證明一個加法范疇為具有擬足夠多內(nèi)射對象的n-阿貝爾范疇當(dāng)且僅當(dāng)它能夠作為n-叢傾斜子范疇嵌入到內(nèi)射上生成的阿貝爾范疇中.
[Abstract]:The higher dimensional theory of algebra representation theory was developed by Iyama et al., which extended the classical Auslander-Reiten theory and introduced n-Auslander algebra [63] and n-Auslander-Reiten translation functor [64]. As a generalization of translation algebra, Guo introduced n-translation algebra and revealed the internal relationship between n-translation algebra and high-dimensional representation theory [56]. In this paper, we mainly discuss two problems: one is to study (n 1)-denoted finite n-Auslander algebra (more general, n-pretranslation cubic algebra) and its Koszul duality translation, periodicity, almost Koszulicity and n-APR inclination, and the other is to characterize n-Auslander algebra by using n-Abel category. The specific organization is as follows: we first study n-translation algebra, in chapter 3, we study n-cubic algebra, and calculate the single-mode projective decomposition of n-cubic algebra and torsional trivial extension algebra. In chapter 4, we introduce (stable) n-pyramid algebra from (n 1)-finite n-Auslander algebra, and study the Koszul property, periodicity and translation property of them and their Kosuzl duality. In chapter 5, we study the mutation of r [n] n. For Koszul algebra whose global dimension is less than or equal to n, if its Kosuzl duality is allowable (n 鈮，
本文編號：2509224
[Abstract]:The higher dimensional theory of algebra representation theory was developed by Iyama et al., which extended the classical Auslander-Reiten theory and introduced n-Auslander algebra [63] and n-Auslander-Reiten translation functor [64]. As a generalization of translation algebra, Guo introduced n-translation algebra and revealed the internal relationship between n-translation algebra and high-dimensional representation theory [56]. In this paper, we mainly discuss two problems: one is to study (n 1)-denoted finite n-Auslander algebra (more general, n-pretranslation cubic algebra) and its Koszul duality translation, periodicity, almost Koszulicity and n-APR inclination, and the other is to characterize n-Auslander algebra by using n-Abel category. The specific organization is as follows: we first study n-translation algebra, in chapter 3, we study n-cubic algebra, and calculate the single-mode projective decomposition of n-cubic algebra and torsional trivial extension algebra. In chapter 4, we introduce (stable) n-pyramid algebra from (n 1)-finite n-Auslander algebra, and study the Koszul property, periodicity and translation property of them and their Kosuzl duality. In chapter 5, we study the mutation of r [n] n. For Koszul algebra whose global dimension is less than or equal to n, if its Kosuzl duality is allowable (n 鈮，
本文編號：2509224
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