Witt代数和Loewner方程的幂矩阵方法
A power matrix approach to the Witt algebra and Loewner equations
摘要：
本文从幂矩阵的观点出发，发展了形式幂级数和导数的理论。引入形式幂级数的Loewner方程。然后，我们证明了矩阵的指数是满射到组的功率矩阵，和系数是整函数的无穷小生成元的许多系数。进一步地，具有常数无穷小生成元的Loewner方程的解的系数可以通过对无穷小幂矩阵求幂而得到。我们还利用形式Loewner方程研究了无穷小生成元的全纯性与指数化矩阵的全纯性之间的关系。
英文摘要：
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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