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

 

Differential algebraic group structures on the plane


Author: Phyllis J. Cassidy
Journal: Proc. Amer. Math. Soc. 80 (1980), 210-214
MSC: Primary 12H05; Secondary 14L15, 20H20
MathSciNet review: 577745
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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

$\displaystyle ({u_1},{u_2})({v_1},{v_2}) = ({u_1} + {v_1},{u_2} + {v_2} + f({u_1},{v_1})),$

where f is a 2-cocycle of $ {G_a}$ into $ {G_a}$.

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1980-0577745-3
PII: S 0002-9939(1980)0577745-3
Keywords: Differential algebraic, Lie algebra, unipotent matrix group, solvable group, solvable Lie algebra, nilpotent Lie algebra, differential field
Article copyright: © Copyright 1980 American Mathematical Society