本文關(guān)鍵詞：Leibniz Pair的形式形變　出處：《安徽大學(xué)》2017年碩士論文　論文類型：學(xué)位論文

  更多相關(guān)文章： Leibniz Pair 形式形變 Leibniz Pair上同調(diào) Leibniz Pair的單側(cè)形變

【摘要】：形變理論是代數(shù)學(xué)中重要研究?jī)?nèi)容之一,它與代數(shù)幾何,代數(shù)表示論,同調(diào)代數(shù),非交換幾何,代數(shù)拓?fù)涞阮I(lǐng)域都有著密切的關(guān)系.在研究Poisson代數(shù)的形變理論時(shí),M.Flato,M.Gerstenhaber和A.A.Vovonov等人于1995年首先引入了Leibniz pair的定義.之后,Leibniz Pair得到了代數(shù)學(xué)家們廣泛的關(guān)注.本文主要研究Leibniz Pair的幾種形式形變理論.第一章,我們主要回顧結(jié)合代數(shù)和Lie代數(shù)的形式形變理論,包括這兩類代數(shù)的形變方程,Hochschild上同調(diào)與Lie代數(shù)的Chevalley-Eilenberg上同調(diào).第二章,我們首先回顧了Leibniz Pair與Leibniz Pair上同調(diào)的定義;其次,我們討論了Leibniz Pair的整體形式形變,即Leibiniz pair中的結(jié)合代數(shù)與Lie代數(shù)同時(shí)形變;最后,我們?cè)敿?xì)證明了Leibniz Pair的整體形變正是由Leibniz Pair上同調(diào)所控制.值得指出的是,M.Flato等人已經(jīng)指出這一事實(shí),但未給出證明.第三章,我們研究了Leibniz Pair的兩種單側(cè)形變,即結(jié)合代數(shù)發(fā)生形變而Lie代數(shù)不作形變,與Lie代數(shù)發(fā)生形變而結(jié)合代數(shù)不作形變.考慮Leibniz Pair雙復(fù)形的兩種譜序列,我們構(gòu)造了兩種新的上同調(diào)群.進(jìn)而通過(guò)討論Leibniz Pair的兩種單側(cè)形變的形變方程,我們證明了這兩種單側(cè)形變由這兩種新的上同調(diào)所控制.
[Abstract]:Deformation theory is one of the important research contents in algebra, which is related to algebraic geometry, algebraic representation theory, homology algebra, noncommutative geometry. In the study of deformation theory of Poisson algebra, M. Flato has a close relationship in the field of algebraic topology. In 1995, M. Gerstenhaber and A. A. Vovonov first introduced the definition of Leibniz pair. Leibniz Pair has been paid more and more attention by mathematicians. In this paper, several formal deformation theories of Leibniz Pair are studied. Chapter 1. We mainly review the formal deformation theory combined with algebra and Lie algebra, including the deformation equations of these two algebras. Hochschild cohomology and Chevalley-Eilenberg cohomology of Lie algebra. Chapter 2. We first review the definition of cohomology between Leibniz Pair and Leibniz Pair. Secondly, we discuss the global deformation of Leibniz Pair, that is, the associative algebra in Leibiniz pair and the Lie algebra at the same time. Finally, we prove in detail that the global deformation of Leibniz Pair is controlled by the cohomology of Leibniz Pair. M. Flato et al. Has pointed out this fact, but has not given the proof. In chapter 3, we study two kinds of unilateral deformation of Leibniz Pair. That is, associative algebras deform but Lie algebras do not deform, and Lie algebras deform and associative algebras do not deform. Two spectral sequences of Leibniz Pair bicomplex are considered. We construct two new cohomology groups, and by discussing the deformation equations of two unilateral deformations of Leibniz Pair, we prove that these two unilateral deformations are controlled by these two cohomology.
【學(xué)位授予單位】：安徽大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2017
【分類號(hào)】：O15

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本文編號(hào)：1394052