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首页> 外文期刊>Jahresbericht der Deutschen Mathematiker-Vereinigung >Patrick Dehornoy, Francois Digne, Eddy Godelle, Daan Krammer, Jean Michel: 'Foundations of Garside Theory' EMS Tracts in Mathematics, vol. 22, EMS, 2015, 710 pp.
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Patrick Dehornoy, Francois Digne, Eddy Godelle, Daan Krammer, Jean Michel: 'Foundations of Garside Theory' EMS Tracts in Mathematics, vol. 22, EMS, 2015, 710 pp.

机译:帕特里克·德霍诺伊(Patrick Dehornoy),弗朗索瓦·迪涅(Francois Digne),埃迪·戈黛尔(Eddy Godelle),达安·克拉默(Daan Krammer),让·米歇尔(Jean Michel):“ Garside理论的基础”数学中的EMS领域,第1卷。 22,EMS,2015,710页

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摘要

In 1925, Emil Artin invented the braid group to understand knots and links. As every conjugacy class in the braid group determines a link, the first challenge was to classify conjugacy classes in the braid group B_n on n strings. Forty years passed, until Frank Arnold Garside (1915-1988) in his 1965 thesis revealed the lattice structure of B_n, which enabled him to solve the conjugacy problem for all n ≥ 3. In particular, he discovered a "fundamental element" Δ ∈ B_n which is normal in the sense that conjugation with Δ maps the cone of positive braid words onto itself. Thus any braid word can be put into a standard form Δ~ma with m ∈ Z where the positive braid a is taken from a finite set. With a little further effort, the conjugacy problem was solved. For n ≥ 3, the centre of B_n is generated by Δ~2.
机译:1925年,埃米尔·阿丁(Emil Artin)发明了编织小组,以了解结和纽带。当编织组中的每个共轭类都确定一个链接时,第一个挑战是在n个字符串上对编织组B_n中的共轭类进行分类。 40年过去了,直到Frank Arnold Garside(1915-1988)在1965年的论文中揭示B_n的晶格结构,这使他能够解决所有n≥3的共轭问题。特别是,他发现了一个“基本元素”Δ∈ B_n在与Δ共轭的意义上是正常的,它将正向编织词的锥体映射到自身上。因此,任何编织词都可以用m∈Z的标准形式Δ〜ma表示,其中正编织a取自有限集。经过进一步的努力,共轭问题得以解决。对于n≥3,B_n的中心由Δ〜2生成。

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