李代数的非交换张量积的对角理想分解
Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal
摘要：
证明了由李代数$L$和$N$构成的$(L,N)$对的非交换张量积$L \otimes N$关于其对角理想$L \square N$和非交换外积$L \wedge N$的分裂定理.两年前，第二作者在特殊病例$N=L$中描述了类似的情况。这种兴趣是由于$L \square N$的大小强烈影响$L \otimes N$的结构。另一个问题通常与$L \otimes N$的结构相关，涉及运算符$\square$相对于自由积形成的行为。在这种情况下，我们用另一个分裂定理来回答，并注意到与同伦理论的一些联系。
英文摘要：
We prove a theorem of splitting for the nonabelian tensor product $L \otimes N$ of a pair $(L,N)$ of Lie algebras $L$ and $N$ in terms of its diagonal ideal $L \square N$ and of the nonabelian exterior product $L \wedge N$. A similar circumstance was described two years ago by the second author in the special case $N=L$. The interest is due to the fact that the size of $L \square N$ influences strongly the structure of $L \otimes N$. Another question, often related to the structure of $L \otimes N$, deals with the behaviour of the operator $\square$ with respect to the formation of free products. We answer with another theorem of splitting even in this case, noting some connections with the homotopy theory.
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