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Bruhat Decomposition for Carpet Subgroups of Chevalley Groups Over Fields

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Algebra and Logic Aims and scope

Necessary and sufficient conditions for a Bruhat decomposition to exist in a carpet subgroup of the Chevalley group over a field defined by an irreducible closed carpet of additive subgroups are established. It turns out that carpet subgroups, which admit the Bruhat decomposition and are distinct from Chevalley groups, are exhausted by groups lying between Chevalley groups of types Bl, Cl, F4 or G2 over various imperfect fields of exceptional characteristics 2 or 3, respectively, of which the larger field is an algebraic extension of the smaller field.

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Author information

Authors and Affiliations

  1. Siberian Federal University, Institute of Mathematics and Fundamental Informatics, Krasnoyarsk, Russia

    Ya. N. Nuzhin

  2. St. Petersburg State University, St. Petersburg, Russia

    A. V. Stepanov

Authors
  1. Ya. N. Nuzhin
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  2. A. V. Stepanov
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Corresponding author

Correspondence to Ya. N. Nuzhin.

Additional information

Translated from Algebra i Logika, Vol. 60, No. 5, pp. 497-509, September-October, 2021. Russian DOI: https://doi.org/10.33048/alglog.2021.60.503.

Ya. N. Nuzhin is supported by Krasnoyarsk Mathematical Center, Agreement with RF Ministry of Education and Science No. 075-02-2020-1534/1, and by RFBR, project No. 19-01-00566.

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Nuzhin, Y.N., Stepanov, A.V. Bruhat Decomposition for Carpet Subgroups of Chevalley Groups Over Fields. Algebra Logic 60, 327–335 (2021). https://doi.org/10.1007/s10469-021-09658-4

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  • DOI: https://doi.org/10.1007/s10469-021-09658-4

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