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Algebraic varieties with group operations given by morphisms, or group objects in the category of algebraic varieties, the category of algebraic schemes, or closely related categories.

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How to find the polynomials that define a compact Matrix Lie group from its Lie algebra?

Consider a compact (connected) Lie group, or more generally, a linear algebraic Lie group. Suppose we are given the Lie algebra corresponding to the Lie group. How can we find a set of polynomial equ …