A note on the Baker--Campbell--Hausdorff series in terms of right-nested\n commutators

2020/06/29 by Ana Arnal, Arnal, Ana, Fernando Casas +3 · 2 citations
Computer Science · Mathematics · #17Bxx #22Exx #Advanced Combinatorial Mathematics #Algebraic structures and combinatorial models #Coding theory and cryptography #FOS: Physical sciences #Mathematical Physics (math-ph)

paper · pdf · doi:10.48550/arxiv.2006.15869

openalex publication_date 2020/06/29 · openalex created_date 2022/07/26 · openalex updated_date 2026/07/28

Abstract

We get compact expressions for the Baker--Campbell--Hausdorff series Z =\n\log( e^X , e^Y) in terms of right-nested commutators. The reduction in the\nnumber of terms originates from two facts: (i) we use as a starting point an\nexplicit expression directly involving independent commutators and (ii) we\nderive a complete set of identities arising among right-nested commutators. The\nprocedure allows us to obtain the series with fewer terms than when expressed\nin the classical Hall basis at least up to terms of grade 10.\n

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