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 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 Resource, created by Eric W. Weisstein. https://mathworld.wolfram.com/AlgebraicGroup.html