Hasse–schmidt derivations and cayley–hamilton theorem for exterior algebras

Letterio Gatto, Inna Scherbak

Research output: Chapter in Book/Report/Conference proceedingChapterpeer-review

Abstract

Using the natural notion of Hasse–Schmidt derivations on an exterior algebra, we relate two classical and seemingly unrelated subjects. The first is the famous Cayley–Hamilton theorem of linear algebra, “each endomor-phism of a finite-dimensional vector space is a root of its own characteristic polynomial”, and the second concerns the expression of the bosonic vertex operators occurring in the representation theory of the (infinite-dimensional) Heisenberg algebra.

Original languageEnglish
Title of host publicationFunctional analysis and geometry
Subtitle of host publicationSelim Grigorievich Krein centennial
PublisherAmerican Mathematical Society
Pages149-165
Number of pages17
ISBN (Electronic)9781470453565
ISBN (Print)9781470437824
DOIs
StatePublished - 2019

Publication series

NameContemporary Mathematics
Volume733
ISSN (Print)0271-4132
ISSN (Electronic)1098-3627

Keywords

  • Hasse-Schmidt Derivations on Grassmann Algebras
  • Theorem of Cayley and Hamilton
  • Vertex Operators

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