本文選題：Gorenstein導(dǎo)出范疇　切入點：Gorenstein導(dǎo)出函子　出處：《西北民族大學(xué)》2017年碩士論文

【摘要】：由Grothendieck-Verdier在上個世紀(jì)60年代引入了導(dǎo)出范疇的概念,在代數(shù)表示論和代數(shù)幾何等領(lǐng)域取得巨大成功.2010年高楠和章璞引入了 Gorenstein導(dǎo)出范疇并得到了 Gorenstein導(dǎo)出范疇的一些基本結(jié)論.而后高楠對Gorenstein導(dǎo)出范疇,奇點范疇,Gorenstein導(dǎo)出等價,三角粘合進行了一系列研究.伊朗學(xué)者Asadolahi也在Gorenstein導(dǎo)出范疇中得到了許多令人滿意的結(jié)論.本文由三部分組成.第一部分主要介紹本文所需的三角范疇,Gorenste:in同調(diào)代數(shù)和表示論的一些基本結(jié)論.第二部分給出了 Gorenstein導(dǎo)出范疇的兩個等價定義,并考慮了 Gorenstein導(dǎo)出函子,得到了 Gorenstein導(dǎo)出函子存在性的一個充分條件.第三部分給出了一些經(jīng)典結(jié)論在Gorenstein導(dǎo)出范疇中的推廣得到了幾個結(jié)論首先得到了:定理3.1.9若三角函子θ:g((?)→D(?)(A)是稠密的,則(?)-dimA∞,其中(?)是A的一個反變有限子范疇此外還得到了有限維代數(shù)的有界Gorenstein導(dǎo)出范疇中Auslander-Rieten三角存在的充要條件,考慮了 CM有限代數(shù)的Gorenstein導(dǎo)出等價并給出了一個Gorenstein導(dǎo)出范疇的三角粘合.
[Abstract]:The concept of 60s by Grothendieck-Verdier in the last century introduced the derived category, in the representation theory of algebras and algebraic geometry and other fields have achieved great success in.2010 high Pu Nan and chapter introduced Gorenstein derived category and some basic conclusions are obtained. Then Gorenstein derived category of Gao Nan Gorenstein derived category, singularity categories, Gorenstein derived equivalence, triangle the adhesive has carried out a series of research. Iran scholar Asadolahi has also been a lot of satisfactory results in the Gorenstein derived category. This paper consists of three parts. The first part mainly introduces the triangulated category required, Gorenste:in said some basic conclusions and homological algebra theory. The second part presents two equivalent definitions of Gorenstein derived categories and, considering the Gorenstein derived functor, and obtain a sufficient condition for the existence of Gorenstein derived functor. The third part gives the extension of some classical conclusions in Gorenstein derived category in the first several conclusions obtained: theorem 3.1.9 if the functor delta theta: G ((?), D (?) (A) is dense, then (?) -dimA 2, which (? A) is a counter variable the sub category also has finite dimensional algebras have necessary and sufficient conditions for the existence of Auslander-Rieten triangle Gorenstein derived category in the considered CM finite algebra Gorenstein derived equivalence and gives a triangular Gorenstein derived category of bonding.

【學(xué)位授予單位】：西北民族大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2017
【分類號】：O154.1

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