超势的准均匀性

摘要：

本文研究了特征为零的代数闭域上完备自由代数中超势的拟齐性。证明了有限维Jacobi代数的超势右等价于加权齐次超势的充要条件是Jacobi代数的0阶Hochschlid同调群中的相应类为零.这个结果可以看作是著名的孤立超曲面奇性定理Kyoji Saito的一个非交换版本。

英文摘要：

In this article, we study the quasi-homogeneity of a superpotential in a complete free algebra over an algebraic closed field of characteristic zero. We prove that a superpotential with finite dimensional Jacobi algebra is right equivalent to a weighted homogeneous superpotential if and only if the corresponding class in the 0-th Hochschlid homology group of the Jacobi algebra is zero. This result can be viewed as a noncommutative version of the famous theorem of Kyoji Saito on isolated hypersurface singularities.

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