Cyclic relations and the Goldberg coefficients in the Campbell-Baker-Hausdorff formula

Thompson, Robert C.

doi:10.1090/S0002-9939-1982-0663855-0

Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

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Cyclic relations and the Goldberg coefficients in the Campbell-Baker-Hausdorff formula
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by Robert C. Thompson PDF

Proc. Amer. Math. Soc. 86 (1982), 12-14 Request permission

Abstract:

Recursively defined coefficients for the commutator-free form of the Campbell-Baker-Hausdorff formula are shown to apply to the commutator version of this formula, and a new relation on these coefficients is derived.

References

Karl Goldberg, The formal power series for $\textrm {log}\,e^xe^y$, Duke Math. J. 23 (1956), 13–21. MR 82571
Nathan Jacobson, Lie algebras, Interscience Tracts in Pure and Applied Mathematics, No. 10, Interscience Publishers (a division of John Wiley & Sons, Inc.), New York-London, 1962. MR 0143793