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“Two Lie groups having isomorphic Lie algebras are locally isomorphic. The

local Lie subgroups of the Lie group are determined by the subalgebras of

the Lie algebra. If the Lie group is locally simple, that is, if it has no

locally defined invariant Lie subgroup, the Lie algebra is simple, that is,

it has no ideal except itself and the zero ideal.”—B.L. van der Waerden’s

HISTORY OF ALGEBRA, p.166.

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