非交换有理函数与边界环的Farber不变量
Noncommutative Rational Functions and Farber's Invariants of Boundary Links
摘要：
在[2] M. Farber用非交换有理函数代数中的值构造了m分量边界链的不变量。在本文中，我们简化了他的结构，并表示它们使用的非交换推广的行列式介绍Gelfand和Retakh。特别地，对于m元非交换多项式代数上的每个有限维模N，我们构造了一个特征有理幂级数chi（N）。若N是任意特征的代数闭域且N是半单的，则级数chi（N）决定N.
英文摘要：
In [2] M. Farber constructed invariants of m-component boundary links with values in algebra of noncommutative rational functions. In this paper we simplify his constructions and express them by using noncommutative generalizations of determinants introduced by Gelfand and Retakh. In particular, for every finite-dimensional module N over the algebra of noncommutative polynomials of m variables we construct a characteristic rational power series chi(N). If N is an algebraically closed field of arbitrary characteristic and N is semisimple, the series chi(N) determines N.
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