Hasse-Schmidt Derivations on Grassmann Algebras / IMPA Monographs Bd.4 (PDF)
- Lastschrift, Kreditkarte, Paypal, Rechnung
- Kostenloser tolino webreader
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 describingthe 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.
Parham Salehyan graduated from Sharif University of Technology, Iran, and received his PhD in mathematics from the IMPA, Brazil, in 2003. He holds a permanent position at the Department of Mathematics of São Paulo State University - Unesp, São José do Rio Preto Campus. His research interests lie in algebraic geometry, mainly in the theory of Weierstrauss points on families of curves and, more recently, in the algebro-combinatorial aspects related to Schubert calculus.
- Autoren: Letterio Gatto , Parham Salehyan
- 2016, 1st ed. 2016, 195 Seiten, Englisch
- Verlag: Springer-Verlag GmbH
- ISBN-10: 331931842X
- ISBN-13: 9783319318424
- Erscheinungsdatum: 08.07.2016
Abhängig von Bildschirmgröße und eingestellter Schriftgröße kann die Seitenzahl auf Ihrem Lesegerät variieren.
- Dateiformat: PDF
- Größe: 2.41 MB
- Ohne Kopierschutz
- Vorlesefunktion
“It is entirely self-contained, and at the same time advanced in that it touches on many different areas in the fields of differential equations and mathematical physics and has further notes and references at the end of every chapter, as well as exercises highlighting further connections. … This book will be welcomed not only by scholars interested in generalized global coordinate-free settings, but also by students wishing to become acquainted with advanced areas of multilinear algebra and their applications.” (Rabe von Randow, zbMATH 1350.15001, 2017)
Schreiben Sie einen Kommentar zu "Hasse-Schmidt Derivations on Grassmann Algebras / IMPA Monographs Bd.4".
Kommentar verfassen