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Hasse-Schmidt Derivations on Grassmann Algebras = With Applications to Vertex Operators /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Hasse-Schmidt Derivations on Grassmann Algebras/ by Letterio Gatto, Parham Salehyan.
其他題名:	With Applications to Vertex Operators /
作者:	Gatto, Letterio.
其他作者:	Salehyan, Parham.
面頁冊數:	XXIV, 195 p. 16 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Matrix theory. -
電子資源:	https://doi.org/10.1007/978-3-319-31842-4
ISBN:	9783319318424

Hasse-Schmidt Derivations on Grassmann Algebras = With Applications to Vertex Operators /
Gatto, Letterio.

Hasse-Schmidt Derivations on Grassmann AlgebrasWith Applications to Vertex Operators /[electronic resource] :by Letterio Gatto, Parham Salehyan. - 1st ed. 2016. - XXIV, 195 p. 16 illus.online resource. - IMPA Monographs ;4. - IMPA Monographs ;3.

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 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.

ISBN: 9783319318424

Standard No.: 10.1007/978-3-319-31842-4doiSubjects--Topical Terms:

1023862
Matrix theory.

LC Class. No.: QA184-205

Dewey Class. No.: 512.5

Hasse-Schmidt Derivations on Grassmann Algebras = With Applications to Vertex Operators /
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