TY - CHAP

T1 - Hasse–schmidt derivations and cayley–hamilton theorem for exterior algebras

AU - Gatto, Letterio

AU - Scherbak, Inna

N1 - Publisher Copyright:
©2019 American Mathematical Society.
Copyright:
Copyright 2020 Elsevier B.V., All rights reserved.

PY - 2019

Y1 - 2019

N2 - 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.

AB - 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.

KW - Hasse-Schmidt Derivations on Grassmann Algebras

KW - Theorem of Cayley and Hamilton

KW - Vertex Operators

UR - http://www.scopus.com/inward/record.url?scp=85078729165&partnerID=8YFLogxK

U2 - 10.1090/conm/733/14739

DO - 10.1090/conm/733/14739

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AN - SCOPUS:85078729165

SN - 9781470437824

T3 - Contemporary Mathematics

SP - 149

EP - 165

BT - Functional analysis and geometry

PB - American Mathematical Society

ER -