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Original Articles

Commutative post-Lie algebra structures on Kac–Moody algebras

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Pages 5218-5226 | Received 07 Feb 2019, Accepted 05 Apr 2019, Published online: 22 May 2019
 

Abstract

We determine commutative post-Lie algebra structures on some infinite-dimensional Lie algebras. We show that all commutative post-Lie algebra structures on loop algebras are trivial. This extends the results for finite-dimensional perfect Lie algebras. Furthermore, we show that all commutative post-Lie algebra structures on affine Kac–Moody Lie algebras are “almost trivial”.

2010 MATHEMATICS SUBJECT CLASSIFICATION:

Acknowledgement

Thanks are due to the referee for helpful remarks which improved the presentation.

Additional information

Funding

Dietrich Burde is supported by the Austrian Science Foundation FWF, grant P28079 and grant I3248.

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