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Semisimple Lie groups admitting a free algebra of invariants

Assume we work over an algebraically closed field of characteristic zero. I know that for a connected semisimple algebraic group there is an upper bound for the number of isomorphism classes of ...
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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 ...
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