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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)


Subgroups of $ ax+b$ and the splitting of triangular group schemes

Author: William C. Waterhouse
Journal: Proc. Amer. Math. Soc. 79 (1980), 520-522
MSC: Primary 14L17; Secondary 20G15
MathSciNet review: 572293
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Abstract: The subgroup schemes of the $ ax + b$ group are computed. This leads to a quick proof that a triangular group scheme over an algebraically closed field is a semidirect product of unipotent and diagonalizable subgroups.

References [Enhancements On Off] (What's this?)

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  • [2] Armand Borel, Linear algebraic groups, Notes taken by Hyman Bass, W. A. Benjamin, Inc., New York-Amsterdam, 1969. MR 0251042 (40 #4273)
  • [3] Michel Demazure and Pierre Gabriel, Groupes algébriques. Tome I: Géométrie algébrique, généralités, groupes commutatifs, Masson & Cie, Éditeur, Paris; North-Holland Publishing Co., Amsterdam, 1970 (French). Avec un appendice Corps de classes local\ par Michiel Hazewinkel. MR 0302656 (46 #1800)
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  • [5] John Brendan Sullivan, A decomposition theorem for pro-affine solvable algebraic groups over algebraically closed fields, Amer. J. Math. 95 (1973), 221–228. MR 0360614 (50 #13061)

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Additional Information

PII: S 0002-9939(1980)0572293-9
Article copyright: © Copyright 1980 American Mathematical Society

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