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 few years ago 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 \(L \otimes N\).
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Acknowledgements
We thank the referees for their comments. The fourth author (F.G.R.) acknowledges NRF (South Africa) for the Grant Nos. CPRR 14071175245 and CSUR 93652. The third author was supported by a grant from Ferdowsi University of Madhhad-Graduate Studys (No. 31659).
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Communicated by Miin Huey Ang.
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Niroomand, P., Johari, F., Parvizi, M. et al. Decomposition of the Nonabelian Tensor Product of Lie Algebras via the Diagonal Ideal. Bull. Malays. Math. Sci. Soc. 42, 1295–1304 (2019). https://doi.org/10.1007/s40840-017-0540-6
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DOI: https://doi.org/10.1007/s40840-017-0540-6