Topologically Simple, Totally Disconnected, Locally Compact Infinite Matrix Groups

P. Groenhout; G. A. Willis; C. D. Reid

doi:10.5802/jolt.1146

P. Groenhout; G. A. Willis; C. D. Reid

Journal of Lie Theory, Volume 30 (2020) no. 4, pp. 965-980

Abstract

We construct uncountably many non-locally isomorphic examples of topologically simple nondiscrete totally disconnected locally compact groups. The new examples differ from known examples of such groups in that they have trivial quasi-centre, but also have infinite abelian locally normal subgroups. The examples are constructed as almost upper-triangular matrices modulo scalar matrices over finite fields, where "almost upper-triangular" is defined with respect to one of an uncountable family of preorders generalising the natural orders on the set of integers and the set of natural numbers.

arXiv Zbl

DOI: 10.5802/jolt.1146

Classification: 22D05, 20H30, 20E18
Keywords: Infinite matrix, finite field, locally compact group, topologically simple, quasi-centre

@article{JOLT_2020_30_4_a3,
     author = {P. Groenhout and G. A. Willis and C. D. Reid},
     title = {Topologically {Simple,} {Totally} {Disconnected,} {Locally} {Compact} {Infinite} {Matrix} {Groups}},
     journal = {Journal of Lie Theory},
     pages = {965--980},
     year = {2020},
     volume = {30},
     number = {4},
     doi = {10.5802/jolt.1146},
     zbl = {1475.22010},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.1146/}
}

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P. Groenhout; G. A. Willis; C. D. Reid. Topologically Simple, Totally Disconnected, Locally Compact Infinite Matrix Groups. Journal of Lie Theory, Volume 30 (2020) no. 4, pp. 965-980. doi: 10.5802/jolt.1146

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