1963/10/01 by James Cheng‐Chung Wei · 4 citations
Mathematics · Computer Science · #Advanced Topics in Algebra #Polynomial and algebraic computation #Mathematics #Hausdorff space #Algebra over a field #Formal power series #Lie algebra #Associative property #Pure mathematics #Product (mathematics) #Exponential map (Riemannian geometry) #Exponential function #Associative algebra #Operator (biology) #Power series #Algebra representation #Division algebra #Mathematical analysis
paper · doi:10.1063/1.1703910
openalex publication_date 1963/10/01 · openalex created_date 2025/10/10 · openalex updated_date 2026/05/21
The Baker-Hausdorff theorem states that for two given elements x and y in an associative algebra, the equation exey = ez has a solution z which lies in the Lie algebra generated by x and y. The Magnus continuous analog gives an exponential solution to a linear operator differential equation. Both theorems are valid globally for free Lie algebras of formal power series. For algebras that are not free, however, both theorems are locally but not globally valid. Some examples are given. Necessary and sufficient conditions for global validity are discussed. A superior representation in terms of a finite product of exponentials is also given.