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＜E-Book＞
Hasse-Schmidt Derivations on Grassmann Algebras : With Applications to Vertex Operators / by Letterio Gatto, Parham Salehyan
(IMPA Monographs ; 4)

Edition	1st ed. 2016.
Publisher	(Cham : Springer International Publishing : Imprint: Springer)
Year	2016
Language	English
Size	XXIV, 195 p. 16 illus : online resource
Authors	*Gatto, Letterio author Salehyan, Parham author SpringerLink (Online service)
Subjects	LCSH:Algebras, Linear LCSH:Differential equations LCSH:Operator theory FREE:Linear Algebra FREE:Differential Equations FREE:Operator Theory
Notes	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 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 HTTP:URL=https://doi.org/10.1007/978-3-319-31842-4

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