外代数上的 Hasse--Schmidt 导子与 Cayley--Hamilton 定理
环与代数
2019-01-10 v1 表示论
摘要
利用外代数上{\em Hasse--Schmidt 导子}的自然概念，我们将两个经典且看似无关的课题联系起来。其一是线性代数中著名的 Cayley--Hamilton 定理，“{\em 有限维向量空间的每个自同态都是其自身特征多项式的根}”，其二是（无限维）Heinsenberg 代数表示论中出现的玻色顶点算子的表达。
引用
@article{arxiv.1901.02686,
title = {Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior Algebras},
author = {Letterio Gatto and Inna Scherbak},
journal= {arXiv preprint arXiv:1901.02686},
year = {2019}
}
备注
to appear in Cont. Math. ("Selim Krein Centennial"), 17 pages, Collaboration has been supoorted by the Politecnico di Torino Programme "Finanziamento diffuso della Ricerca", the University of Tel Aviv which hosted the first author, partially supported by INDAM-GNSAGA and "PRIN: Geometria delle variet\`a algebriche"