Hasse-Schmidt derivations on Grassmann algebras [electronic resource] : with applications to vertex operators / Letterio Gatto, Parham Salehyan.
Gatto, Letterio, author.; Salehyan, Parham, author.
2016
QA325
Available Online

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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
Published Switzerland : Springer, 2016.
Language English
Description 1 online resource (xxiv, 195 pages) : illustrations.
Call Number QA325
Dewey Decimal Classification 515/.33
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.
Access Note 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.
Linked Resources Online Access
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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.

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