Abstract.
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
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Dedicated to the memory of Daniel Arnaudon
Submitted: January 30, 2006; Accepted: March 8, 2006
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Zuevsky, A. Non-Commutative Ricci and Calabi Flows. Ann. Henri Poincaré 7, 1569–1578 (2006). https://doi.org/10.1007/s00023-006-0293-5
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DOI: https://doi.org/10.1007/s00023-006-0293-5