论文标题
谎言元素和矩阵树定理
Lie elements and the matrix-tree theorem
论文作者
论文摘要
对于G组G的有限维表示V，我们介绍并研究了代数K [G]组中谎言元件的概念。 Lie元素的L（V）\ subset K [g]是谎言代数和作用于原始表示V的G模块。 谎言元素通常表现出不错的组合特性。因此，对于g = s_n和v，置换表示形式，我们证明了类似于经典矩阵树定理的谎言元件的特征多项式的公式。
For a finite-dimensional representation V of a group G we introduce and study the notion of a Lie element in the group algebra k[G]. The set L(V) \subset k[G] of Lie elements is a Lie algebra and a G-module acting on the original representation V. Lie elements often exhibit nice combinatorial properties. Thus, for G = S_n and V, a permutation representation, we prove a formula for the characteristic polynomial of a Lie element similar to the classical matrix-tree theorem.
