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., 
) are examples of algebraic groups.
Algebraic Group
See also
Free Group, Group, Lie GroupThis entry contributed by Gregory Woodhouse
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References
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.Referenced on Wolfram|Alpha
Algebraic GroupCite this as:
Woodhouse, Gregory. "Algebraic Group." From MathWorld--A Wolfram Web Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AlgebraicGroup.html