Algebraic Group

An algebraic group is a variety (or scheme) endowed with a group structure such that the group operations are morphisms of varieties (or schemes). The concept is similar to that of a Lie group except that the underlying operations are required to be algebraic (locally representable in terms of polynomials) rather than differentiable. Complex linear groups (e.g., SL(n,C)) are examples of algebraic groups.

See also

Free Group, Group, Lie Group

This entry contributed by Gregory Woodhouse

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Humphreys, J. E. Linear Algebraic Groups. New York: Springer-Verlag, 1981.Itô, K. (Ed.). "Algebraic Groups." §13 in Encyclopedic Dictionary of Mathematics, 2nd ed., Vol. 1. Cambridge, MA: MIT Press, pp. 42-53, 1986.Springer, T. A. Linear Algebraic Groups. Boston: Birkhäuser, 1981.Weil, A. Adèles and Algebraic Groups. Princeton, NJ: Princeton University Press, 1961.

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Algebraic Group

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Woodhouse, Gregory. "Algebraic Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein.

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