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 Group
*This 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 Group## Cite this as:

Woodhouse, Gregory. "Algebraic Group." From *MathWorld*--A Wolfram Web Resource, created by Eric
W. Weisstein. https://mathworld.wolfram.com/AlgebraicGroup.html