Hasse-Schmidt Derivations on Grassmann Algebras

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.

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.

"It provides a comprehensive advanced multi-linear algebra course based on the concept of Hasse-Schmidt derivations on a Grassmann algebra ... . It covers a wealth of important material in a concise, nevertheless instructive manner, and as such it may serve as an excellent guide to further, more advanced and detailed reading in this fundamental area of contemporary mathematics." (Ahmed Lesfari, Mathematical Reviews, June, 2017)

"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 highlightingfurther 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)