A power matrix approach to the Witt algebra and Loewner equations

Details A power matrix approach to the Witt algebra and Loewner equations A power matrix approach to the Witt algebra and Loewner equations

2009-07-09

arxiv.org/abs/0907.1601v1

Mathematics

Complex Variables

25 pages

Scientific paper

The theory of formal power series and derivation is developed from the point of view of the power matrix. A Loewner equation for formal power series is introduced. We then show that the matrix exponential is surjective onto the group of power matrices, and the coefficients are entire functions of finitely many coefficients of the infinitesimal generator. Furthermore coefficients of the solution to the Loewner equation with constant infinitesimal generator can be obtained by exponentiating an infinitesimal power matrix. We also use the formal Loewner equations to investigate the relation between holomorphicity of an infinitesimal generator to holomorphicity of the exponentiated matrix.

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