Hasse–Schmidt derivations and Cayley–Hamilton theorem for exterior algebras
| Autor: | Letterio Gatto, Inna Scherbak |
|---|---|
| Jazyk: | angličtina |
| Rok vydání: | 2019 |
| Předmět: |
Pure mathematics
Endomorphism Hasse-Schmidt Derivaions on an Exterior Algebra Hasse-Schmidt Derivaions on an Exterior Algebra Cayley-Hamilton Theorem Vertex Operators Cayley-Hamilton Theorem Representation theory Vertex (geometry) Vertex Operators Linear algebra Exterior algebra Cayley–Hamilton theorem Mathematics Vector space Characteristic polynomial |
| Popis: | Using the natural notion of {\em Hasse--Schmidt derivations on an exterior algebra}, we relate two classical and seemingly unrelated subjects. The first is the celebrated Cayley--Hamilton theorem of linear algebra, "{\em 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) Heinsenberg algebra. |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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