GICAR代数中的闭Lie理想

Lie Ideals in GICAR Algebra

本文给出了GICAR代数中闭Lie理想的完全刻画.设A是GICAR代数,L是A的闭Lie理想,则存在A的闭理想J,使得[A,J]=[J,J](?) L (?) π-1(Z(A/J)),其中π是A到A/J上的商映射.反之,任意这种形式的闭子空间L是A的闭Lie理想.

We give a detailed description of the structure of a Lie ideal in GICAR algebra. Let A be the GICAR algebra, L be a closed Lie ideal of A. Then there is a closed ideal J of A such that [ J, J] L π-1(Z(A/J)), where π is the canonical quotient mapping from A onto A/J. On the other hand, every closed linear subspace L of A of this from is a Lie ideal of A.