Exponentiation of commuting nilpotent varieties

• Paul Sobaje ^[1]
  1. [1] University of Melbourne

     University of Melbourne

     Australia

     
• Localización: Journal of pure and applied algebra, ISSN 0022-4049, Vol. 219, Nº 6 (June 2015), 2015, págs. 2206-2217
• Idioma: inglés
• DOI: 10.1016/j.jpaa.2014.07.031
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• Resumen

  • Let Hbe a linear algebraic group over an algebraically closed field of characteristic p >0. We prove that any “exponential map” for Hinduces a bijection between the variety of r-tuples of commuting [p]-nilpotent elements in Lie(H)and the variety of height rinfinitesimal one-parameter subgroups of H. In particular, we show that for a connected reductive group Gin pretty good characteristic, there is a canonical exponential map for Gand hence a canonical bijection between the aforementioned varieties, answering in this case questions raised both implicitly and explicitly by Suslin, Friedlander, and Bendel.