Simplifying the Reinsch algorithm for the Baker–Campbell–Hausdorff series

DOI10.1063/1.4939929zbMath1367.17001arXiv1501.05034OpenAlexW3098618800WikidataQ59619434 ScholiaQ59619434MaRDI QIDQ2795588

Alexander Van-Brunt, Matt Visser

Publication date: 21 March 2016

Published in: Journal of Mathematical Physics (Search for Journal in Brave)

Full work available at URL: https://arxiv.org/abs/1501.05034

Mathematics Subject Classification ID

Structure theory for Lie algebras and superalgebras (17B05) Finite-dimensional groups and algebras motivated by physics and their representations (81R05) Computational methods for problems pertaining to nonassociative rings and algebras (17-08)

Related Items (10)

Explicit Baker-Campbell-Hausdorff expansions ⋮ An algorithm for the Baker-Campbell-Hausdorff formula ⋮ Wilson loops on Riemann surfaces, Liouville theory and covariantization of the conformal group ⋮ Computing the Riemannian Logarithm on the Stiefel Manifold: Metrics, Methods, and Performance ⋮ A Matrix-Algebraic Algorithm for the Riemannian Logarithm on the Stiefel Manifold under the Canonical Metric ⋮ Cumulants, spreadability and the Campbell-Baker-Hausdorff series ⋮ Exact Baker–Campbell–Hausdorff formula for the contact Heisenberg algebra ⋮ Classification of commutator algebras leading to the new type of closed Baker-Campbell-Hausdorff formulas ⋮ The algebra of complex 2 × 2 matrices and a general closed Baker–Campbell–Hausdorff formula ⋮ An exact power series representation of the Baker–Campbell–Hausdorff formula

Cites Work

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• The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin
• Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin
• The formal power series for \(\log\,e^x e^y\)
• Explicit Baker-Campbell-Hausdorff expansions
• On the convergence and optimization of the Baker-Campbell-Hausdorff formula
• A simple expression for the terms in the Baker–Campbell–Hausdorff series
• An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
• Numerical values of Goldberg’s coefficients in the series for 𝑙𝑜𝑔(𝑒^{𝑥}𝑒^{𝑦})
• Cyclic Relations and the Goldberg Coefficients in the Campbell-Baker- Hausdorff Formula
• Special-case closed form of the Baker–Campbell–Hausdorff formula

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