Hasse-Schmidt derivations on Grassmann algebras [electronic resource] : with applications to vertex operators / Letterio Gatto, Parham Salehyan.
2016
QA325
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Title
Hasse-Schmidt derivations on Grassmann algebras [electronic resource] : with applications to vertex operators / Letterio Gatto, Parham Salehyan.
Author
Gatto, Letterio, author.
ISBN
9783319318424 (electronic book)
331931842X (electronic book)
9783319318417
331931842X (electronic book)
9783319318417
Published
Switzerland : Springer, 2016.
Language
English
Description
1 online resource (xxiv, 195 pages) : illustrations.
Call Number
QA325
Dewey Decimal Classification
515/.33
512.5
512.5
Summary
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.
Bibliography, etc. Note
Includes bibliographical references and index.
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Access limited to authorized users.
Source of Description
Online resource; title from PDF title page (SpringerLink, viewed July 18, 2016).
Added Author
Salehyan, Parham, author.
Series
IMPA monographs ; v. 4.
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Table of Contents
Prologue
Generic Linear Recurrence Sequences
Algebras and Derivations
Hasse-Schmidt Derivations on Exterior Algebras
Schubert Derivations
Decomposable Tensors in Exterior Powers
Vertex Operators via Generic LRS
Index.
Generic Linear Recurrence Sequences
Algebras and Derivations
Hasse-Schmidt Derivations on Exterior Algebras
Schubert Derivations
Decomposable Tensors in Exterior Powers
Vertex Operators via Generic LRS
Index.