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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2024 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Differential algebraic group structures on the plane
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by Phyllis J. Cassidy
Proc. Amer. Math. Soc. 80 (1980), 210-214
DOI: https://doi.org/10.1090/S0002-9939-1980-0577745-3

Abstract:

The differential algebraic group structures on the affine line and plane are classified. The additive group ${G_a}$ of the coefficient field is the only differential algebraic group structure on the line. Every differential algebraic group with underlying set in the plane is unipotent and is isomorphic to a group whose law of composition is defined by the formula \[ ({u_1},{u_2})({v_1},{v_2}) = ({u_1} + {v_1},{u_2} + {v_2} + f({u_1},{v_1})),\] where f is a 2-cocycle of ${G_a}$ into ${G_a}$.
References
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Bibliographic Information
  • © Copyright 1980 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 80 (1980), 210-214
  • MSC: Primary 12H05; Secondary 14L15, 20H20
  • DOI: https://doi.org/10.1090/S0002-9939-1980-0577745-3
  • MathSciNet review: 577745