Hasse-Schmidt Derivations on Grassmann Algebras: With Applications to Vertex Operators by Gatto, Letterio

Hasse-Schmidt Derivations on Grassmann Algebras: With Applications to Vertex Operators (Paperback) (ISBN-13: 9783319811345)

Vendor: Letterio Gatto
Product type: Books
Format: Paperback
$129.99
$129.99
$129.99
Subtotal: $129.99
Hasse-Schmidt Derivations on Grassmann Algebras: With Applications to Vertex Operators by Gatto, Letterio

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

$129.99
Hasse-Schmidt Derivations on Grassmann Algebras: With Applications to Vertex Operators by Gatto, Letterio

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

$129.99
Format: Paperback
Description
Description
x
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.


Author: Letterio Gatto, Parham Salehyan
ISBN-10: 3319811347
ISBN-13: 9783319811345
Publisher: Springer
Language: English
Published: 05/31/2018
Pages: 195
Format: Paperback
Weight: 0.69lbs
Size: 9.21h x 6.14w x 0.46d
By Letterio Gatto
By Letterio Gatto
x
Letterio Gatto received his PhD in mathematics from the University of Torino in 1993, and since then has held permanent positions at the Department of Mathematical Sciences of the Politecnico di Torino. He is currently associate professor at the Politecnico, where he offers courses on linear algebra and geometry for students in Engineering. His research interests range from Schubert calculus (classical, equivariant and quantum), algebraic curves and moduli (families of Weierstrauss points and jets of line bundles on Gorenstein curves) and integrable systems from the algebro-geometrical point of view.
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.

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