This categorical fact enables a definition of hopf monoids in some setups that do not allow a sensible. Over fields it has been shown by sweedler that the existence of integrals in a hopf algebra is equivalent to the hopf algebra being finite dimensional. The representation theory of a hopf algebra is particularly nice, since the. Hopf algebras, quantum groups and topological eld theory. Bulletin of the ams this book should be very useful as a comprehensive, up to date introduction to the algebraic aspects of hopf algebras. Hopf algebras and their representation categories 2.
Montgomery, hopf algebras and their actions on rings, cmbs reg. Buy hopf algebras and their actions on rings cbms regional conference series in. In this chapter we introduce the notion of a hopf algebra over a field k as a bialgebra with an additional map called the coinverse or antipode. Hopf algebras occur naturally in algebraic topology, where they originated and are related to the hspace concept, in group scheme theory, in group theory via the concept of a group ring, and in numerous other places, making them probably the most familiar type of bialgebra. This book brings together many of these recent developments from the viewpoint of the algebraic structure of hopf algebras and their actions and coactions. A logos is a ringlike structure and the theory of logoi has many things in common with the theory. Hopf algebras and their actions on rings pdf free download. Hopf algebras and their actions on rings susan montgomery. Susan montgomery usc dornsife university of southern california. In many respects, kg is the example that is generalized in the concept of hopf algebra. These are notes for a course held in summer semester 2010 on the ludwigmaximillian university munich.
Click download or read online button to get hopf algebras and their actions on rings book now. Hopf algebras and their actions on rings, including automorphism groups of algebras, and quantum groups. In mathematics, a hopf algebra, named after heinz hopf, is a structure that is simultaneously an unital associative algebra and a counital coassociative coalgebra, with these structures compatibility making it a bialgebra, and that moreover is equipped with an antiautomorphism satisfying a certain property. The focus, however, will lay on structures relevant also to modern. Hopf algebras and their actions on rings extended selected. In this paper, ore extensions in the class of hopf algebras are studied. This site is like a library, use search box in the widget to get ebook that you want. Integrals in hopf algebras are an essential tool in studying finite dimensional hopf algebras and their action on algebras. Quantum groups are treated as an important example, rather than as an end in themselves. Hopf algebras generating fusion rings and topological invariants simon lentner abstract. Einstein chair mathematics seminar the graduate center, cuny. This content was uploaded by our users and we assume good faith they have the permission to share this book.
In this paper we examine how much of this is true for hopf algebras over rings. Get your kindle here, or download a free kindle reading app. Hopf algebras and their actions on rings ams bookstore. There are some other ones which i know are out there, but i havent read. Hopf algebras and their actions on rings, by susan montgomery. We discuss some basic features of hopf algebras and give some initial examples, including the group ring kg. Montgomery, hopf algebras and their actions on rings, cbms, no. Chapters 47 are devoted to four of the most beautiful hopf algebras currently known.
The course primarily constitutes an elementary, yet mathematically rigid introduction to the theory of hopf algebras. Lecture course hopf algebras, quantum groups and topological field. This one is more about the theory of hopf algebras than about drinfeldjimbo. Hopf algebras and their actions on rings cbms regional. This one is more about the theory of hopf algebras than about drinfeldjimbo quantum groups. Hopf algebras are also studied in their own right, with much work.