Minimality of the Special Linear Groups

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Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, quotient groups, and subgroups. Minimality of SLn(F) is concluded by appealing to the associated Lie group decomposition as ... continued below

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iv, 83 leaves

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Hayes, Diana Margaret December 1997.

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  • Hayes, Diana Margaret

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Let F denote the field of real numbers, complex numbers, or a finite algebraic extension of the p-adic field. We prove that the special linear group SLn(F) with the usual topology induced by F is a minimal topological group. This is accomplished by first proving the minimality of the upper triangular group in SLn(F). The proof for the upper triangular group uses an induction argument on a chain of upper triangular subgroups and relies on general results for locally compact topological groups, quotient groups, and subgroups. Minimality of SLn(F) is concluded by appealing to the associated Lie group decomposition as the product of a compact group and an upper triangular group. We also prove the universal minimality of homeomorphism groups of one dimensional manifolds, and we give a new simple proof of the universal minimality of S∞.

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iv, 83 leaves

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  • December 1997

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  • March 26, 2014, 9:30 a.m.

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  • Aug. 25, 2014, 10:19 a.m.

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Hayes, Diana Margaret. Minimality of the Special Linear Groups, dissertation, December 1997; Denton, Texas. (digital.library.unt.edu/ark:/67531/metadc279280/: accessed August 20, 2018), University of North Texas Libraries, Digital Library, digital.library.unt.edu; .