In algebraic geometry, an algebraic group (or group variety) is a group that is an algebraic variety, such that the multiplication and inverse are given by regular functions on the variety. In category theoretic terms, an algebraic group is a group object in the category of algebraic varieties.
Read more about Algebraic Group: Classes, Algebraic Subgroup, Coxeter Groups
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“I have no scheme about it,—no designs on men at all; and, if I had, my mode would be to tempt them with the fruit, and not with the manure. To what end do I lead a simple life at all, pray? That I may teach others to simplify their lives?—and so all our lives be simplified merely, like an algebraic formula? Or not, rather, that I may make use of the ground I have cleared, to live more worthily and profitably?”
—Henry David Thoreau (1817–1862)
“We begin with friendships, and all our youth is a reconnoitering and recruiting of the holy fraternity they shall combine for the salvation of men. But so the remoter stars seem a nebula of united light, yet there is no group which a telescope will not resolve; and the dearest friends are separated by impassable gulfs.”
—Ralph Waldo Emerson (1803–1882)