Téléchargez le livre : Hasse-Schmidt Derivations on Grassmann Algebras

Hasse-Schmidt Derivations on Grassmann Algebras

With Applications to Vertex Operators de

,

Éditeur :

Springer


Collection :

IMPA Monographs

Paru le : 2016-07-08

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Description
This book provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra (an analogue of the Taylor expansion for real-valued functions), and shows how this notion provides a natural framework for many ostensibly unrelated subjects: traces of an endomorphism and the Cayley-Hamilton theorem, generic linear ODEs and their Wronskians, the exponential of a matrix with indeterminate entries (Putzer's method revisited), universal decomposition of a polynomial in the product of two monic polynomials of fixed smaller degree, Schubert calculus for Grassmannian varieties, and vertex operators obtained with the help of Schubert calculus tools (Giambelli's formula). Significant emphasis is placed on the characterization of decomposable tensors of an exterior power of a free abelian group of possibly infinite rank, which then leads to the celebrated Hirota bilinear form of the Kadomtsev-Petviashvili (KP) hierarchy describing the Plücker embedding of an infinite-dimensional Grassmannian. By gathering ostensibly disparate issues together under a unified perspective, the book reveals how even the most advanced topics can be discovered at the elementary level.
Pages
195 pages
Collection
IMPA Monographs
Parution
2016-07-08
Marque
Springer
EAN papier
9783319318417
EAN EPUB
9783319318424
Informations sur l'ebook
Nombre pages copiables
1
Nombre pages imprimables
19
Taille du fichier
3666 Ko
Prix
116,04 €

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