Grassmann and Stiefel Varieties Over Composition Algebras

Golasiński, Marek, Gómez Ruiz, Francisco

Grassmann and Stiefel Varieties Over Composition Algebras
  • 出版商: Springer
  • 出版日期: 2024-08-18
  • 售價: $6,040
  • 貴賓價: 9.5 折 $5,738
  • 語言: 英文
  • 頁數: 334
  • 裝訂: Quality Paper - also called trade paper
  • ISBN: 3031364074
  • ISBN-13: 9783031364075

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商品描述

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.

商品描述(中文翻譯)

本專著探討矩陣流形，即其元素可以自然表示為矩陣陣列的流形。經典的矩陣流形（Stiefel、Grassmann 和旗流形）在更一般的背景下進行研究。它提供了工具來研究在畢達哥拉斯形式實數域上的矩陣變量。書中的內容相對自成體系，包含了一些對於從事微分幾何、黎曼幾何以及其他數學領域的研究者來說有用的非平凡結果。該書也旨在讓已修習代數幾何和微分幾何入門課程的研究生能夠輕鬆閱讀。

作者簡介

Marek Golasiński 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 Toruń (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 Toruń (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.

作者簡介(中文翻譯)

Marek Golasiński 自2012年以來擔任波蘭奧爾什丁的瓦爾米亞和馬祖里大學數學與計算機科學系教授。他在1971年至2011年間曾擔任波蘭托倫的哥白尼大學數學與計算機科學系副教授。他於1978年獲得博士學位，並於2004年獲得資格認證，兩者均為代數拓撲領域，均來自波蘭托倫的哥白尼大學數學與計算機科學系。他曾與 Juno Mukai 合著一本書，內容涉及圓球的 Gottlieb 和 Whitehead 中心群、射影空間及 Moore 空間。

Francisco Gómez Ruiz 在巴塞隆納大學學習數學。1978年，他在多倫多大學獲得博士學位（他的指導教授是 Stephen Halperin）。在巴塞隆納自治大學數學系工作兩年後，他又在坎塔布里亞大學工作一年，隨後在馬拉加大學的代數、幾何與拓撲系任教33年。他已發表超過30篇研究文章和3本書籍。

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