| Abstrakt: |
Let A = ℝ 〈 a 1 , ... , a n 〉 and B = ℝ 〈 b 1 , ... , b n 〉 be the semigroup rings spanned on the right zero semigroup RZ n = { a 1 , ... , a n } , and on the left zero semigroup LZ n = { b 1 , ... , b n } , respectively, together with the identity element 1. We suggest a closed formula solving the equation w = log (e u e v) which is the evolution of the Campbell–Baker–Hausdorff formula given by the Hausdorff series w = H (u , v) = u + v + 1 2 [ u , v ] + 1 1 2 [ u , [ u , v ] ] + 1 1 2 [ v , [ v , u ] ] + ⋯ , where [ u , v ] = u v − v u , in the algebras A and B. [ABSTRACT FROM AUTHOR] |
