Frontiers of Mathematics in China

, Volume 14, Issue 2, pp 421–433 | Cite as

On multivariable Zassenhaus formula

  • Linsong Wang
  • Yun Gao
  • Naihuan JingEmail author
Research Article


We give a recursive algorithm to compute the multivariable Zassenhaus formula \({e^{{X_1} + {X_2} + \cdots + {X_n}}} = {e^{{X_1}}}{e^{{X_2}}} \ldots {e^{{X_n}}}\prod{_{k=2}^\infty}e^W{_k}\) and derive an effective recursion formula of Wk.


Baker-Campbell-Hausdorff formula Zassenhaus formula 


22E05 16W25 16S20 


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N. Jing’s work was partially supported by the National Natural Science Foundation of China (Grant No. 11531004) and Simons Foundation (Grant No. 523868).


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Copyright information

© Higher Education Press and Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.School of MathematicsSouth China University of TechnologyGuangzhouChina
  2. 2.Department of Mathematics and StatisticsYork UniversityTorontoCanada
  3. 3.Department of MathematicsNorth Carolina State UniversityRaleighUSA

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