NODEM98 abstracts

Algebraic foundations of noncommuting flows M. Kawski (Arizona State University)
Noncommuting flows are at the very heart of the Crouch-Grossman algorithm (and variations thereof) for integrating differential equations with algebraic constraints. As generally no relations may be known a-priori, it is natural to work in a free Lie algebra setting. We present the combinatorial and algebraic foundations of noncommuting exponential product expansions. Specifically, we demonstrate that the most fundamental structure governing such noncommuting flows is the "chronological algebra" (dual of a Leibniz algebra). Its symmetrization yields the better known shuffle algebra. Chronological calculus determines and explains precisely which iterated integrals have to be considered in expansions using a minimal number of terms.

Algebraic foundations of noncommuting flows
M. Kawski
(Arizona State University)

Noncommuting flows are at the very heart of the Crouch-Grossman algorithm (and variations thereof) for integrating differential equations with algebraic constraints. As generally no relations may be known a-priori, it is natural to work in a free Lie algebra setting.

We present the combinatorial and algebraic foundations of noncommuting exponential product expansions. Specifically, we demonstrate that the most fundamental structure governing such noncommuting flows is the "chronological algebra" (dual of a Leibniz algebra). Its symmetrization yields the better known shuffle algebra. Chronological calculus determines and explains precisely which iterated integrals have to be considered in expansions using a minimal number of terms.