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Complete Reducibility In Euclidean Twin Buildings

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Abstract

In [6], J.P. Serre defined completely reducible subcomplexes of spherical buildings in order to study subgroups of reductive algebraic groups. This paper begins the exploration of how one may use a similar notion of completely reducible subcomplexes of twin buildings to study subgroups of algebraic groups over a ring of Laurent polynomials and Kac-Moody groups. In this paper we explore the definitions of convexity and complete reducibility in twin buildings and some implications of the two in the Euclidean case.

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2011-08-31

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Buildings; Complete Reducibility; twin buildings

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Brown, Kenneth Stephen

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Vogtmann, Karen L
Speh, Birgit Else Marie

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Mathematics

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Ph. D., Mathematics

Degree Level

Doctor of Philosophy

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Government Document

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dissertation or thesis

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