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Calculations in exceptional groups over rings

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In the present paper, we discuss a major project whose goal is to develop theoretical background and working algorithms for calculations in exceptional Chevalley groups over commutative rings. We recall some basic facts concerning calculations in groups over fields, and indicate complications arising in the ring case. Elementary calculations as such are no longer conclusive. We describe the basics of calculations with elements of exceptional groups in their minimal representations, which allow one to reduce calculations in the group itself to calculations in subgroups of smaller rank. For all practical purposes, such calculations are much more efficient than localization methods. Bibliography: 147 titles.

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Authors and Affiliations

  1. St. Petersburg State University, St. Petersburg, Russia

    A. Luzgarev & N. Vavilov

  2. Abdus Salam School of Mathematical Sciences at the GCU, Lahore, Pakistan

    A. Stepanov

Authors
  1. A. Luzgarev
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  2. A. Stepanov
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  3. N. Vavilov
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Correspondence to A. Luzgarev.

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Published in Zapiski Nauchnykh Seminarov POMI, Vol. 373, 2009, pp. 48–72.

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Luzgarev, A., Stepanov, A. & Vavilov, N. Calculations in exceptional groups over rings. J Math Sci 168, 334–348 (2010). https://doi.org/10.1007/s10958-010-9984-z

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  • DOI: https://doi.org/10.1007/s10958-010-9984-z

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