LIE ELEMENTS AND THE MATRIX-TREE THEOREM

被引：0

作者：

Burman, Yurii ^{[1
,2
]}

Kulishov, Valeriy ^{[3
]}

机构：

[1] Res Univ, Higher Sch Econ, 6 Usacheva Str, Moscow 119048, Russia

[2] Independent Univ Moscow, 11 Bvlassievsky Per, Moscow 119002, Russia

[3] Natl Res Univ, Higher Sch Econ, Moscow, Russia

来源：

MOSCOW MATHEMATICAL JOURNAL | 2023年 / 23卷 / 01期

关键词：

Matrix-tree theorem; multigraphs; generalized de-terminants;

D O I：

10.17323/1609-4514-2023-23-1-47-58

中图分类号：

O29 [应用数学];

学科分类号：

070104 ;

摘要：

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) & SUB; 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. In partic-ular, we prove a formula, similar to the classical matrix-tree theorem, for the characteristic polynomial of a Lie element in the permutation representation V of the group G = Sn.

引用

页码：47 / 58

页数：12

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