Fee Hopf

From the preface: "Hopf algebras, Hopf fibration of spheres, Hopf-Rinow complete Riemannian manifolds, Hopf theorem on the ends of groups - can one imagine modern mathematics without all this? Many ot

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.

Hopf algebras have important connections to quantum theory, Lie algebras, knot and braid theory, operator algebras and other areas of physics and mathematics. They have been intensely studied in the past; in particular, the solution of a number of conjectures of Kaplansky from the 1970s has led to progress on the classification of semisimple Hopf algebras and on the structure of pointed Hopf algebras. Among the topics covered are results toward the classification of finite-dimensional Hopf algebras (semisimple and non-semisimple), as well as what is known about the extension theory of Hopf algebras. Some papers consider Hopf versions of classical topics, such as the Brauer group, while others are closer to work in quantum groups. The book also explores the connections and applications of Hopf algebras to other fields.

Only book on Hopf algebras aimed at advanced undergraduates

Radford (U. of Illinois-Chicago) presents a graduate textbook on Hopf algebras over a field k that can also be use as a reference by researchers in Hopf algebras and related areas. It reflects the dee

《非線性系統Hopf分岔回饋控制》主要研究典型的三維和四維非線性系統的Hopf分岔控制問題，分析系統的分岔特性，提出控制方法，設計分岔控制器，使系統產生所期望的動力學行為。 首先綜述非線性控制理論、分岔控制、Hopf分岔控制以及混沌控制等的研究現狀與發展狀況。然後介紹非線性動力學研究的一些基本概念和幾種分岔控制方法，闡述Hopf分岔定義與判據、Hopf分岔理論、以及Hopf分岔週期解的近似

本書介紹Hopf群餘代數的基礎知識和**研究成果. 全書共分八章，第一章是必要的概念及準備，第二、三、四章分別介紹擬三角Hopf群餘代數和餘擬三角Hopf群代數的構造，第五章介紹Radford群雙積，並討論其上的自同構，第六章討論Hopf群餘代數的偏作用，第七章討論群餘環的函子可分性、Galois理論及Morita關係，第八章介紹弱Hopf群代數及其表示.本書可供高等院校數學和數學物理專業的高年級

本書介紹偏Hopf作用的表示、偏纏繞結構，偏Doi-Hopf群模、以及積分的基本概念和理論，重點討論這些模上的Maschke定理、可分函子、Frobenius性質及其應用等。本書內容由淺入深，既有理論又有新的應用，反映了近10年來偏Hopf作用理論研究的最新成果。

The concept of Hopf algebras was first introduced in the theory of algebraic topology but in recent years has been developed by many mathematicians and applied to other areas of mathematics such as Lie groups, algebraic groups and Galois theory. This book is an introduction to the basic theory of Hopf algebras for the reader already familiar with the basic ideas of linear algebra and commutative algebra. After introducing and discussing the basic properties of coalgebras, bialgebras and Hopf algebras, the author treats the fundamental structure theorem of bi-modules and Sullivan's proof of the existence and uniqueness of integrals of Hopf algebras. This book will interest graduate students and research workers who specialise in algebra.

This text aims to provide graduate students with a self-contained introduction to topics that are at the forefront of modern algebra, namely, coalgebras, bialgebras and Hopf algebras. The last chapter

The volume is almost entirely composed of the research and expository papers by the participants of the International Workshop "Groups, Rings, Lie and Hopf Algebras", which was held at the Memorial Un

本書主要介紹了群胚、擬群、箭圖、乘子、環擴張以及與之相關的各類Hopf型代數的基本概念和理論，尤其討論了弱乘子Hopf代數概念的發展、構造以及對偶理論。

Summarizes the proceedings and keynote presentations from a conference held in Brussels, Belgium. This work focuses on results in classical Hopf algebras as well as the classification theory of finite

The two basic building units carbon and hydrogen can be combined in a million different ways to give a plethora of fascinating organic compounds. Henning Hopf presents not only the most remarkable str

This is the first book to be dedicated entirely to Drinfeld's quasi-Hopf algebras. Ideal for graduate students and researchers in mathematics and mathematical physics, this treatment is largely self-contained, taking the reader from the basics, with complete proofs, to much more advanced topics, with almost complete proofs. Many of the proofs are based on general categorical results; the same approach can then be used in the study of other Hopf-type algebras, for example Turaev or Zunino Hopf algebras, Hom-Hopf algebras, Hopfish algebras, and in general any algebra for which the category of representations is monoidal. Newcomers to the subject will appreciate the detailed introduction to (braided) monoidal categories, (co)algebras and the other tools they will need in this area. More advanced readers will benefit from having recent research gathered in one place, with open questions to inspire their own research.

This advanced research monograph is devoted to the Wiener-Hopf technique, a function-theoretic method that has found applications in a variety of fields, most notably in analytical studies of diffract

In this deeply researched book Ted Hopf challenges contemporary theorizing about international relations. He advances what he believes is a commonsensical notion: a state's domestic identity has an en

《Hopf代數表示範疇中的Monoidal不變量(英文)》在Hopf代數表示範疇層面引入一些新的monoidal不變量，這些不變量包括表示範疇的Green環、Casimir數、高階Frobenius-Schur指標、Grothendieck環、某種類型的多元齊次多項式等。著作主要研究這些不變量在Hopf代數表示理論中所發揮的作用，揭示這些不變量與Hopf代數表示範疇中其它重要研究對象之間的關係，通過具體實例展示這些不變量的具體表現形式等。這些不變量的引入為人們研究Hopf代數表示範疇的結構與分類提供了新的工具，也為人們深入理解與研究monoidal範疇提供了新的視角。《Hopf代數表示範疇中的Monoidal不變量(英文)》所展示的一些研究成果對於推動代數表示理論體系的發展與完善，促進Hopf代數、張量範疇等數學分支的交叉與融合具有積極的作用。

A gripping new novel from one of the best-known names in survivalist fiction. Former Marine-turned-author, G. Michael Hopf grabs readers from page one with his breathtaking blend of action, adventure

This book is addressed to graduate students and research workers in theoretical physics who want a thorough introduction to group theory and Hopf algebras. It is suitable for a one-semester course in