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arXiv · 1502.00417

Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal

P. Niroomand·F. Johari·M. Parvizi·F. G. Russo
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Abstract

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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P. Niroomand, F. Johari, M. Parvizi, F. G. Russo. 2015-02-02. Decomposition of the nonabelian tensor product of Lie algebras via the diagonal ideal. https://doi.org/10.1007/s40840-017-0540-6

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