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- W178282895 abstract "This chapter is devoted to the construction of the “maximal” Kac—Moody group Ç associated to a Kac—Moody Lie algebra g = g(A), for A any£x£GCM, due to Tits. There are other versions of groups associated to g(A), e.g., we will discuss the “minimal” Kac—Moody group gmindefined by Kac—Peterson in Section 7.4. We first construct certain groupsB,Nand {Pi}1<i<e, and then G is constructed as the amalgamated product of these groups. We now give an outline of the construction of these groups. Let n C g be the positive part of g, i.e., the direct sum of positive root spaces of g. Consider the completion û of n got by taking the directproductof the positive root spaces. Then ñ is canonically a pro-nilpotent pro-Lie algebra. LetUbe the pro-unipotent pro-group with Liel f =ñ (guaranteed by Theorem 4.4.19). Similarly, let Ui, 1 < i <Q, be the pro-unipotent pro-group with Lie algebra Lie Ui= ûi, where û;C ñ is the direct product of all the positive root spaces except the one corresponding to the simple roota i ." @default.
- W178282895 created "2016-06-24" @default.
- W178282895 creator A5016007541 @default.
- W178282895 date "2002-01-01" @default.
- W178282895 modified "2023-10-03" @default.
- W178282895 title "Kac-Moody Groups" @default.
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- W178282895 doi "https://doi.org/10.1007/978-1-4612-0105-2_6" @default.
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