Differential algebraic group structures on the plane
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- by Phyllis J. Cassidy PDF
- Proc. Amer. Math. Soc. 80 (1980), 210-214 Request permission
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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- Michel Lazard, Sur la nilpotence de certains groupes algébriques, C. R. Acad. Sci. Paris 241 (1955), 1687–1689 (French). MR 75210
Additional 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