Hasse--Schmidt Derivations and Cayley--Hamilton Theorem for Exterior\n Algebras

2019/01/09 by Letterio Gatto, Gatto, Letterio, Inna Scherbak +1
Computer Science · Mathematics · #15A75 #17B69. 050E5 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Matrix Theory and Algorithms #Representation Theory (math.RT) #Rings and Algebras (math.RA)

paper · pdf · doi:10.48550/arxiv.1901.02686

openalex publication_date 2019/01/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28

Abstract

Using the natural notion of em Hasse--Schmidt derivations on an exterior\nalgebra, we relate two classical and seemingly unrelated subjects. The first\nis the celebrated Cayley--Hamilton theorem of linear algebra, " em each\nendomorphism of a finite-dimensional vector space is a root of its own\ncharacteristic polynomial", and the second concerns the expression of the\nbosonic vertex operators occurring in the representation theory of the\n(infinite-dimensional) Heinsenberg algebra.\n

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