李元与矩阵树定理

IF 0.6 4区数学 Q3 MATHEMATICS

Moscow Mathematical Journal Pub Date : 2020-11-20 DOI:10.17323/1609-4514-2023-23-1-47-58

Yurii Burman, V. Kulishov

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引用次数: 1

摘要

对于群G的有限维表示V，我们引入并研究了群代数k[G]中李元的概念。李元的集合L(V) \子集k[G]是一个李代数和一个作用于原始表示V的G模。因此，对于置换表示G = S_n和V，我们证明了李元的特征多项式的一个类似于经典矩阵树定理的公式。

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Lie Elements and the Matrix-Tree Theorem

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.

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来源期刊

Moscow Mathematical Journal 数学-数学

CiteScore

1.40

自引率

0.00%

发文量

审稿时长

>12 weeks

期刊介绍： The Moscow Mathematical Journal (MMJ) is an international quarterly published (paper and electronic) by the Independent University of Moscow and the department of mathematics of the Higher School of Economics, and distributed by the American Mathematical Society. MMJ presents highest quality research and research-expository papers in mathematics from all over the world. Its purpose is to bring together different branches of our science and to achieve the broadest possible outlook on mathematics, characteristic of the Moscow mathematical school in general and of the Independent University of Moscow in particular. An important specific trait of the journal is that it especially encourages research-expository papers, which must contain new important results and include detailed introductions, placing the achievements in the context of other studies and explaining the motivation behind the research. The aim is to make the articles — at least the formulation of the main results and their significance — understandable to a wide mathematical audience rather than to a narrow class of specialists.