Non-Commutative Ricci and Calabi Flows

Starting from an improved version of the bicomplex structure associated the continual Lie algebra with non-commutative base algebra, we obtain dynamical systems resulting from the bicomplex conditions. General expressions for conserved currents associated to a continual Lie algebra bicomplex are found explicitly in two first orders. The Moyal-product counterparts for two-dimensional Ricci and Calabi flow equations depending on non-commutative variables are introduced. Communicated by Petr Kulish Dedicated to the memory of Daniel Arnaudon Submitted: January 30, 2006; Accepted: March 8, 2006