【和山数学论坛第403期】美英国帝国理工学院/三峡大学Alexander A.lvanov教授学术报告

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一、报告题目:THE THOMPSON GROUP: OPENING A PATH TO MODERN GROUP THEORY

二、报告人:Alexander A. lvanov 教授

三、时 间:2024328() 14:30-15:10

四、地 点:闻理园A4-216


报告摘要:We enhance the Thompson–Smith construction of the Thompson sporadic simple group E. As a result, (a) we obtain a conceptual explanation of the dichotomy between Lie and finite cases in terms of representations on an (L2(8) : 3)-subgroup; (b) along with 25 · L5(2) and 2+1+8 · A9, we construct in E subgroups 3D4(2) : 3, (F21 × L3(2)) : 2, (G2(3) × 3) : 2 and U3(8) : 6; (c) we consider the coset geometry of the above subgroups and identify the corresponding geometric presentation with that by Havas–Soicher–Wilson; (d) this amounts to a geometric construction and uniqueness proof for E (the uniqueness issue for the Thompson group was listed6 as one of just two outstanding in the Classification of Finite Simple Groups); (e) we deliver an elementary self-contained construction of the Dempwolff–Thompson orthogonal decomposition on the E8-Lie algebra, along with the stabiliser 25+10 ·L5(2) of this decomposition in the Lie group E8(C). The work was further stimulated by the recent reappearance of E in the Moonshine context.


报告人简介:Alexander A. Ivanov,英国帝国理工学院教授三峡大学特聘研究员,博士毕业于莫斯科物理技术学院,1990年国际数学家大会45分钟报告人。主要从事群论、代数组合和代数图论方面的研究工作,撰写了零散群几何学方面的经典专著《Geometry of Sporadic Groups III》在Invent. MathJ. London Math. Soc.Trans. Amer. Math. Soc.Israel J. Math.J. Algebra等期刊发表学术论文100余篇。


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