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 endomorphism 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.
Hasse–Schmidt derivations and Cayley–Hamilton theorem for exterior algebras / Gatto, Letterio; Scherbak, Inna. - STAMPA. - 733(2019), pp. 149-165. ((Intervento presentato al convegno Voronezh Winter Mathematical School tenutosi a Voronezh nel November 13-19, 2017, (organized by Voronezh University, the Moscow Lomonosov University, and the Steklov Mathematical Institute) [10.1090/conm/733/14739].
Titolo: | Hasse–Schmidt derivations and Cayley–Hamilton theorem for exterior algebras | |
Autori: | ||
Data di pubblicazione: | 2019 | |
Serie: | ||
Abstract: | Using the natural notion of Hasse–Schmidt derivations on an exterior algebra, we relate two class...ical and seemingly unrelated subjects. The first is the famous Cayley–Hamilton theorem of linear algebra, “each endomorphism 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. | |
ISBN: | 9781470437824 9781470453565 | |
Appare nelle tipologie: | 4.1 Contributo in Atti di convegno |
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http://hdl.handle.net/11583/2790492