The early proofs of the theorem of Campbell, Baker, Hausdorff, and Dynkin

DOI10.1007/s00407-012-0095-8zbMath1245.01002OpenAlexW2000235175WikidataQ56212033 ScholiaQ56212033MaRDI QIDQ420535

Rüdiger Achilles, Andrea Bonfiglioli

Publication date: 22 May 2012

Published in: Archive for History of Exact Sciences (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1007/s00407-012-0095-8

zbMATH Keywords

PascalBourbakiHausdorffLie-groups

Mathematics Subject Classification ID

History of mathematics in the 20th century (01A60) History of mathematics in the 19th century (01A55) Research exposition (monographs, survey articles) pertaining to history and biography (01-02) History of topological groups (22-03)

Related Items

A group-theoretic approach to the disentanglement of generalized squeezing operators, Explicit Baker-Campbell-Hausdorff expansions, Comments on noncommutative quantum mechanical systems associated with Lie algebras, An explicit Maclaurin series solution to a classic non-autonomous abstract evolution equation, The flow method for the Baker-Campbell-Hausdorff formula: exact results, On expansions for nonlinear systems error estimates and convergence issues, Quantum information scrambling and entanglement in bipartite quantum states, Optimization of quantum Hamiltonian evolution: From two projection operators to local Hamiltonians, Exact Baker–Campbell–Hausdorff formula for the contact Heisenberg algebra, Anomalies in time-ordered products and applications to the BV-BRST formulation of quantum gauge theories, Simplifying the Reinsch algorithm for the Baker–Campbell–Hausdorff series, On the Baker-Campbell-Hausdorff Theorem: non-convergence and prolongation issues, 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

• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Unnamed Item
• Topics in noncommutative algebra. The theorem of Campbell, Baker, Hausdorff and Dynkin
• On Lie supergroups and superbundles defined via the Baker-Campbell-Hausdorff formula
• The Lie theory of connected pro-Lie groups. A structure theory for pro-Lie algebras, pro-Lie groups, and connected locally compact groups
• Convergence of the Magnus series
• Towards a Lie theory of locally convex groups
• Balls and metrics defined by vector fields. I: Basic properties
• On Sophus Lie's fundamental theorem
• Convergence proof for Goldberg's exponential series
• A note on the Campbell-Hausdorff formula
• Jacobi and the birth of Lie's theory of groups
• An elementary proof of the Baker-Campbell-Hausdorff-Dynkin formula
• Subelliptic estimates and function spaces on nilpotent Lie groups
• Hypoelliptic differential operators and nilpotent groups
• On the convergence of exponential operators-the Zassenhaus formula, BCH formula and systematic approximants
• Quasinilpotent Banach-Lie algebras are Baker-Campbell-Hausdorff
• Goldberg's theorem and the Baker-Campbell-Hausdorff formula
• Emergence of the theory of Lie groups. An essay in the history of mathematics 1869--1926
• On the convergence and optimization of the Baker-Campbell-Hausdorff formula
• Lie group structures on quotient groups and universal complexifications for infinite-dimensional Lie groups
• Hypoelliptic second order differential equations
• A new proof of the Baker-Campbell-Hausdorff formula
• Explicit solution of the continuous Baker-Cambell-Hausdorff problem and a new expression for the phase operator
• Hilbert--Schmidt groups as infinite-dimensional Lie groups and their Riemannian geometry
• Die linearen Beziehungen zwischen höheren Kommutatoren
• A connection between the Baker-Hausdorff formula and a problem of Burnside
• A simple expression for the terms in the Baker–Campbell–Hausdorff series
• Convergence of the exponential Lie series
• Convergence domains for the campbell-baker-hausdorff formula
• Démonstration algébrique de la formule de Hausdorff
• Note on the Algebraic Aspect of the Integration of a System of Ordinary Linear Differential Equations
• Some properties of the campbell baker hausdorff series
• Splitting methods
• Pro-Lie groups which are infinite-dimensional Lie groups
• An efficient algorithm for computing the Baker–Campbell–Hausdorff series and some of its applications
• Dynkin’s method of computing the terms of the Baker–Campbell–Hausdorff series
• The Baker-Hausdorff Formula and a Problem in Crystal Physics
• Poincaré and Lie groups
• Cyclic Relations and the Goldberg Coefficients in the Campbell-Baker- Hausdorff Formula
• Lie series and invariant functions for analytic symplectic maps
• On the solution of linear differential equations in Lie groups
• Sur L'Intégrabilité des Sous–Algèbres de lie en Dimension Infinie
• Banach-Lie quotients, enlargibility, and universal complexifications
• Algebras whose groups of units are Lie groups
• Sophus Lie's Third Fundamental Theorem and the Adjoint Functor Theorem
• Maximal reductions in the Baker–Hausdorff formula
• Hardy Spaces on Homogeneous Groups. (MN-28), Volume 28
• Baker-Campbell-Hausdorff formulas
• Magnus and Fer expansions for matrix differential equations: the convergence problem
• The Baker–Campbell–Hausdorff formula and nested commutator identities
• The Baker-Campbell-Hausdorff formula and the convergence of the Magnus expansion
• Sufficient conditions for the convergence of the Magnus expansion
• Geometric Numerical Integration
• On Expanding the Exponential
• Perturbation Theory and Lie Algebras
• Note on the Global Validity of the Baker-Hausdorff and Magnus Theorems
• Expansion of the Campbell‐Baker‐Hausdorff formula by computer
• Properties of Higher-Order Commutator Products and the Baker-Hausdorff Formula
• Exponential Operators and Parameter Differentiation in Quantum Physics
• Normed Lie Algebras
• Mathematical aspects of the quantum theory of fields. Part V. Fields modified by linear homogeneous forces
• Lie groups
• The structure of compact groups. A primer for the student -- a handbook for the expert