Grassmann and Stiefel Varieties over Composition Algebras

Marek Golasiński, Francisco Gómez Ruiz (Autoren)

Buch | Hardcover

XII, 334 Seiten

2023 | 1st ed. 2023
Springer International Publishing (Verlag)
978-3-031-36404-4 (ISBN)

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This monograph deals with matrix manifolds, i.e., manifolds for which there is a natural representation of their elements as matrix arrays. Classical matrix manifolds (Stiefel, Grassmann and flag manifolds) are studied in a more general setting. It provides tools to investigate matrix varieties over Pythagorean formally real fields. The presentation of the book is reasonably self-contained. It contains a number of nontrivial results on matrix manifolds useful for people working not only in differential geometry and Riemannian geometry but in other areas of mathematics as well. It is also designed to be readable by a graduate student who has taken introductory courses in algebraic and differential geometry.

lt;b>Marek Golasinski is a Professor at the Faculty of Mathematics and Computer Science, University of Warmia and Mazury in Olsztyn (Poland) since 2012. He was previously Associate Professor at the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Torun (Poland) from 1971-2011. He was awarded the degrees of Ph.D. (1978) and Habilitation (2004), both in Algebraic Topology from the Faculty of Mathematics and Computer Science, Nicolaus Copernicus University in Torun (Poland). He has written a previous book (with Juno Mukai) on Gottlieb and Whitehead Center Groups of Spheres, Projective and Moore Spaces.

Francisco Gómez Ruiz studied mathematics at the University of Barcelona. In 1978 received his doctorate at the University of Toronto (Stephen Halperin was his advisor). After 2 years at the department of mathematics of the Autonomous University of Barcelona and one year at the University of Cantabria, he has been 33 years professor at the department of algebra, geometry and topology of the University of Malaga. He has published over 30 research articles and 3 books.

- 1. Algebraic Preliminaries. - 2. Exceptional Groups .G2(K) and .F4(K). - 3. Stiefel, Grassmann Manifolds and Generalizations. - 4. More Classical Matrix Varieties. - 5. Algebraic Generalizations of Matrix Varieties. - 6. Curvature, Geodesics and Distance on Matrix Varieties.

Erscheinungsdatum	18.08.2023
Reihe/Serie	RSME Springer Series
Zusatzinfo	XII, 334 p.
Verlagsort	Cham
Sprache	englisch
Maße	155 x 235 mm
Gewicht	621 g
Themenwelt	Mathematik / Informatik ► Mathematik ► Geometrie / Topologie
Schlagworte	Grassmann manifold • Hermitian matrix • Pythagorean Formally Real Field • stiefel manifold • Variety of Idempotent Matrices
ISBN-10	3-031-36404-X / 303136404X
ISBN-13	978-3-031-36404-4 / 9783031364044
Zustand	Neuware