具有连续逆的代数的超维李子代数
Finite-dimensional Lie subalgebras of algebras with continuous inversion
摘要：
研究了有限维李群，其点被连续同态分离成具有连续逆的局部凸代数的可逆元群，且满足适当的完备性条件.我们发现，这些正是线性李群，也就是说，李群可以忠实地表示为矩阵群。我们的方法依赖于证明，某些有限维李代数连续反演交换模的Jacobson根。
英文摘要：
We investigate the finite-dimensional Lie groups whose points are separated by the continuous homomorphisms into groups of invertible elements of locally convex algebras with continuous inversion that satisfy an appropriate completeness condition. We find that these are precisely the linear Lie groups, that is, the Lie groups which can be faithfully represented as matrix groups. Our method relies on proving that certain finite-dimensional Lie subalgebras of algebras with continuous inversion commute modulo the Jacobson radical.
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