An algebraic group over a field 
is an algebraic variety
(or a scheme of finite type over 
) endowed with a group structure
such that the group operations are morphisms over 
. The concept is similar to that of a
Lie group except that the underlying operations are
locally given by regular functions rather than
differentiable functions.
Complex linear algebraic groups (e.g., 
) are examples of algebraic groups.
Algebraic Group
See also
Free Group, Group, Langlands Dual Group, Lie Group, Margulis-Platonov Conjecture, Parabolic Subgroup, Reductive GroupPortions of this entry contributed by Gregory Woodhouse
Explore with Wolfram|Alpha
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, MA: Birkhäuser, 1981.Weil, A. Adèles and Algebraic Groups. Princeton, NJ: Princeton University Press, 1961.Referenced on Wolfram|Alpha
Algebraic GroupCite this as:
Weisstein, Eric W., with contributions by Gregory Woodhouse. "Algebraic Group." From MathWorld--A Wolfram Resource. https://mathworld.wolfram.com/AlgebraicGroup.html