Kassel, christian is the author of quantum groups with isbn 9780387943701 and isbn 0387943706. Introduction to quantum groups george lusztig springer. It is a knot invariant, and we prove its existence and uniqueness given some simple axioms value on the unknot and the socalled skein relations. Coverage also focuses on hopf algebras that produce solutions of the yangbaxter equation and provides an account of drinfelds elegant treatment of the monodromy of the knizhnikzamolodchikov equations. Preliminaries september 17, 2012 talk by ralph klaasse,4pages these are notes to a talk given in the quantum groups seminar during the fall of 2012 at utrecht university, which followed the book quantum groups by kassel. By pierre vogel, in which he extended the tate cohomology to any group. Download citation on analytic analogues of quantum groups in this paper we present a new construction of analytic analogues of quantum groups over. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent fundamental contributions. The theory of quantum groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e.
Kassel quantum groups graduate texts in mathematics 155 springer new york 1995 from math 351 at loyola university chicago. Kassel, quantum groups, graduate texts in mathematics. Quantum groups, christian kassel, gradate texts in mathematics 155, springer, 1995. Quantum groups are noncommutative algebras depending on aparameter q. One of the ideas behind quantum groups is that if we consider a structure that is in a sense equivalent but larger, namely a group algebra or a universal enveloping algebra. Drinfelds quantum double 199 1 bicrossed products of groups 199 2 bicrossed products of bialgebras, 202 3 variations on the adjoint representation 207 4 drinfelds quantum double 2 5 representationtheoretic interpretation of the quantum double 220 6 application to uqsi2 223 7. Kassel, quantum groups, graduate texts in mathematics 155.
Introduction to braid groups university of chicago. Pdf epub high quality, no missing contents and printable compatible devices. Um ihnen ein besseres nutzererlebnis zu bieten, verwenden wir cookies. The discovery of quantum groups was quite unexpected since it was known for a long time that compact groups and semisimple lie algebras are rigid objects, in other words, they cannot be deformed. Introduction, historical survey, hopf algebras, basic.
Pdf introduction to quantum groups download full pdf book. Hopf algebras, quantum groups and topological eld theory winter term 201920. Part four quantum groups and monodromy 383 xvi generalities on quantum enveloping algebras 385. Lectures on quantum groups jens carsten jantzen download. An introduction to quantum groups lectures at ncgoa07 christian. Kac algebras give an example of such structure, but as it turned out their class is too narrow to accommodate the objects arising from drinfeldjimbo deformations. Better still, umn students have online access to the book through the library website.
Introduction to braid groups joshua lieber vigre reu 2011 university of chicago abstract. The story starts from the work of steinitz on the module category of an abelian p group, where. Similarly, the quantum group u q g can be regarded as an algebra over the field qq, the field of all rational functions of an indeterminate q over q see below in the section on quantum groups at q 0. Kassel quantum groups graduate texts in mathematics 155. Quantum groups graduate texts in mathematics 155 by. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with.
The center of quantum group can be described by quantum determinant. Pdf quantum groups download full pdf book download. Knot theory and quantum groups dominic goulding march 3, 2010. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with canonical basis with rather remarkable properties.
See all 7 formats and editions hide other formats and editions. Kassel, quantum groups, graduate texts in mathematics 155, springer 1995 also errata. Hall algebras and quantum groups reading seminar ws1516 the hall algebra of a nitary category encodes its extension structure. From quantum groups to unitary modular tensor categories. Christian kassel this book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on drinfelds recent fundamental contributions. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. These include lectures on algebraic quantum groups, by ken brown and ken goodearl, lectures on quantum groups, by jens jantzen, introduction to quantum groups, by george lusztig, and quantum groups and their primitive ideals, by anthony joseph. Noncommutative algebra an overview sciencedirect topics. In this wellwritten presentation, motivated by numerous examples and problems.
Drinfeldjimbos quantum enveloping algebra u qsl2, duality with the quantum algebra of functions sl. Lectures on quantum groups jens carsten jantzen since its origin about ten years ago, the theory of quantum groups has become one of the most fascinating topics of modern mathematics, with numerous applications to several sometimes rather disparate areas, including lowdimensional topology and mathematical physics. Quantum groups by christian kassel 2012 1008 paperback jan. The quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof. Coverage also focuses on hopf algebras that produce solutions of the yangbaxter equation and here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be.
Hopf algebras, quantum groups and topological field theory. The phrase quantum jump or quantum leap is now in common usage, and incorrectly too. Section 3 constructs the quantum group at roots of unity. Quantum optimal control theory of photoelectron spectroscopy signature of chirality and theoretical description of multiphoton ionization. The last part is an account of drinfelds elegant treatment of the monodromy of the knizhnikzamolodchikov equations, culminating in the construction of kontsevichs universal knot invariant. Quantum groups graduate texts in mathematics 155 by christian kassel. Quantum groups graduate texts in mathematics by christian kassel quantum groups graduate texts in mathematics by christian kassel pdf, epub ebook d0wnl0ad. After formal definitions and basic theory, the book goes on to cover such topics as quantum enveloping algebras, matrix quantum groups, combinatorics, cross products of various kinds, the quantum double, the semiclassical theory of poissonlie groups, the representation theory, braided groups and applications to qdeformed physics. Graduate texts in mathematics 155, springer, berlin, 1995. An introduction to quantum groups lectures at ncgoa07 christian kassel summary lecture 1. Bangming deng, jie du, brian parshall, jianpan wang, finite dimensional algebras and quantum groups, mathematical surveys and monographs 150, amer. Coverage also focuses on hopf algebras that produce solutions of the yangbaxter equation and provides an account of. When q takes the value 1, then quantum groups specialize to classical objects such as groups of symmetries. Optimizing robust quantum gates in open quantum systems.
Quantum groups and their primitive ideals modern surveys in mathematics 29 by anthony joseph. Cohomological invariant for groups coming from quantum group theory. It presents the quantum groups attached to sl2 as well as the basic concepts of the theory of hopf algebras. The first part presents in detail the quantum groups attached to slsubscript 2 as well as the basic concepts of the theory of hopf algebras. The successes of quantum mechanics have been extraordinary. Hopf algebras, quantum groups and topological eld theory. Quantum group glqn which coacts on a suitably deformed algebra of differential. First, the concepts of the fundamental group of a topological space, con guration space, and exact sequences are brie.
Lecture note series 292 this book has real insight and is nicely divided into individual lectures of reasonable size. From this perspective a quantum group is a cvon neumann algebra with some additional structure making the noncommutative space a group like object. Quantum groups graduate texts in mathematics by kassel, christian and a great selection of related books, art and collectibles available now at. Definition and first examples according to the philosophy of noncommutative geometry, unital calgebras should be thought of as algebras of continuous functions on noncommutative, or quantum, compact spaces. These structure coecients of gro are called the fusion coecients of o and 2. Quantum groups by christian kassel springer gtm 155 a quantum groups primer by shahn majid london math. Quantum groups graduate texts in mathematics by christian kassel quantum groups graduate texts in mathematics by christian kassel here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent fundamental contributions. Drinfeldjimbos quantum enveloping algebra u qsl2, duality with the quantum. Having glanced a little bit at the last two in this list, i found both of them more difficult to read. Knots we discuss the jonesconway polynomial, also known as hom y polynomial. Coverage also focuses on hopf algebras that produce solutions of the yangbaxter equation and provides an account of drinfelds elegant treatment of the monodromy of the.
From quantum groups to unitary modular tensor categories 5 for some nk i. Introduction to quantum groups will be of interest to mathematicians working in the representation theory of lie groups and lie algebras, knot theorists, theoretical physicists, and graduate students. Christian kassel quantum groups with 88 illustrations springerverlag. Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. At the same time this quantum group can be interpreted as the quantisation of a particle moving in a curved geometry with blackholelike features. Publication date 1995 topics hopf algebras, mathematical physics, quantum groups, topology. Quantum groups graduate texts in mathematics 155 9780387943701 by kassel, christian and a great selection of similar new, used and collectible books available now at great prices. This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on drinfelds recent fundamental contributions. Very useful for understanding and research in quantum groups, in particular, the chapters on the braid group action and crystal bases highly recommended to all research mathematicians working in quantum groups the writing is one of the most pleasant attributes of this book.
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