The term quantum group first appeared in the theory of quantum integrable systems, which was then formalized by vladimir drinfeld and michio jimbo as a particular class of hopf algebra. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent fundamental contributions. Knots we discuss the jonesconway polynomial, also known as hom y polynomial. Joint work with christophe reutenauer we define a selfmap pal. Hopf algebras, quantum groups and topological eld theory. The geometry of a compact matrix quantum group is a special case of a noncommutative geometry. The lie algebra uqsl2 is given a detailed treatment by the author when q is not a. Compact matrix quantum groups are abstract structures on which the continuous functions on the structure are given by elements of a calgebra. It is designed for teaching and can be used in the advanced students lab or for demonstration experiments in lectures on quantum mechanics. Quantum groups, extracted by drinfeld 1 from applications of the quantum inverse scattering method to quantum integrable systems, are quantizations of the poissonhopf algebras of functions on poissonlie groups 2. Tensor product question in kassel s quantum groups.
The same term is also used for other hopf algebras that deform or are close to classical lie groups or lie algebras, such as a bicrossproduct class of. References are given for quantum groups based on the other lie groups, such as the orthogonal and symplectic groups. It may be checked that the braid group relations are satisfied and this formula indeed defines a group action of b n on x. V g turaev this book provides a concise introduction to quantum groups, braided monoidal categories, and quantum invariants of knots and of threedimensional manifolds. Batch import allows you to combine multiple files at once. 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. Kassel, quantum groups, graduate texts in mathematics.
It also covers recent developments in noncommutative geometry, which have close relations to quantization and quantum group symmetries. Introduction, historical survey, hopf algebras, basic. Kassel, quantum groups, graduate texts in mathematics 155. Convert to pdf or convert from pdf, the merging is entirely up to you.
Quantum groups graduate texts in mathematics 155 by christian kassel. Ams transactions of the american mathematical society. An elementary introduction graduate texts in mathematics applications of lie groups to. Quantum analogs is an experiment to model quantum mechanical wave phenomena with sound waves. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with. We show how to define invariants of graphs related to quantum sl 2 when the graph has more then one connected component and components are colored by blocks of representations with zero quantum. As central objects in knot theory and 3dimensional. We use cookies to offer you a better experience, personalize content, tailor advertising, provide social media features, and better understand the use of our services. Lectures on quantum groups american mathematical society. Drinfelds original icm86 talk quantum groups is something must read, scanned.
Introduction and physical motivations 3 there is a second approach to quantum groups. Their association with permutations has led to their presence in a number of mathematical fields and physics. By pierre vogel, in which he extended the tate cohomology to any group. Quantum groups and noncommutative spaces perspectives on. Kassel, quantum groups, springerverlag, berlin, 1995.
This book is an introduction to the theory of quantum groups. An introduction to quantum groups lectures at ncgoa07 christian kassel summary lecture 1. Modified real structures for quantum groups and applications. This thesis is brought to you for free and open access by the student.
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. This book provides an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and on. 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. 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. Introduction to braid groups university of chicago. Kassel quantum groups graduate texts in mathematics 155. Pdf introduction to quantum groups download full pdf. If gis a connected, simply connected lie group, g can be reconstructed from the universal enveloping algebra ug of the.
Quantum groups graduate texts in mathematics lie groups, lie algebras, and representations. Such structures play an important role in modern mathematical physics and lead to quantum knot invariants. Weinheim quantum chemistry quantum mechanics in chemistry by melvin hanna problems and solutions for mcquarries quantum chemistry quantum chemistry by sannigrahi pdf free download quantum chemistry by by a. Braids and braid groups, the focus of this text, have been at the heart of important mathematical developments over the last two decades. It presents the quantum groups attached to sl2 as well as the basic concepts of the theory of hopf algebras. Jensen university of kassel quantum mechanics ii ss 2012 exercises in quantum mechanics ii assignment 4 please deliver your homework in the postbox. Introduction to braid groups joshua lieber vigre reu 2011 university of chicago abstract. An introduction to the theory of quantum groups ewu digital. Nonstandard comodules for quantum matrix bialgebras. 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.
Direct links to free springer books pdf versions graduate texts in mathematics. Quantum groups are non commutative algebras depending on a parameter q. Michio jimbo considered the algebras with three generators related by the three commutators. At the writing of this thesis the theory of quantum groups is a young and burgeoning. In this wellwritten presentation, motivated by numerous examples and problems, the authors introduce the basic theory of braid groups, highlighting several definitions that show their equivalence. Find materials for this course in the pages linked along the left. What conditions has germany or the eu as a whole attached to the esm loan offer that italy is refusing. The lie algebra uqsl2 is given a detailed treatment by the author when q is not a root of unity. Since poissonlie groups are more or less equivalent to lie bialgebras see 3 for basic definitions and results on quantum groups, one can work instead with quantizations of lie bialgebras.
Pdf introduction to quantum groups download full pdf book. The quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof. Pdf merge combinejoin pdf files online for free soda pdf. Quantum groups, graduate texts in mathematics 155, new york etc. In mathematics, a quantum or quantized enveloping algebra is a qanalog of a universal enveloping algebra. Oct 24, 2016 the free group f 2, the braid group b 3, and palindromes, deuxieme congres canadafrance, uqam, montreal, quebec, canada 2 juin 2008 abstract. A modification of the standard structure on a quasitriangular hopf algebra is introduced by means of which, in particular, the quantum deformation uqsu2 can be endowed with a real structure f. Since poissonlie groups are more or less equivalent to lie bialgebras see 3 for basic definitions and results on quantum groups, one can work instead with. This book is aimed at presenting different methods and perspectives in the theory of quantum groups, bridging between the algebraic, representation theoretic, analytic, and differentialgeometric approaches. The paper used in this book is acidfree and falls within the guidelines. Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. The final prices may differ from the prices shown due to specifics of vat rules. Cohomological invariant for groups coming from quantum group theory. Femtosecond twophoton photoassociation of hot magnesium atoms.
We construct quantum groups at a root of unity and we describe their monoidal module category using techniques from the representation theory of finite dim a quiver quantum group springerlink advertisement. You can also use the full soda pdf online application to convert. Ams proceedings of the american mathematical society. You can read the quantum groups book on our website. Quantum groups graduate texts in mathematics 155 by. Graduate texts in mathematics 155, springer, berlin, 1995. An introduction to quantum groups lectures at ncgoa07 christian. 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 algebra of functions sl. You must be logged in to scitation to activate your free access. This graduatelevel text develops the aspects of group theory most relevant to physics and chemistry such as the theory of representations and illustrates. We carry out a construction of nonstandard matrix quantum groups comodules through a generalization of the coaction on tensor powers of a comodule. Indeed, since omnk is generated as a free algebra by the elements xij 1.
Hopf algebras, quantum groups and topological eld theory winter term 201920. Quantum groups are noncommutative algebras depending on a parameter q. 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. Springer have made a bunch of books available for free. This free one time meeting will include a viewing of debbie fords movie and a lively discussion lead by steven c. Part of the graduate texts in mathematics book series gtm, volume 155 log in to check access.
A quantum dynamical study using thermal random phase wavefunctions. Saieswari amaran, ronnie kosloff, michal tomza, wojciech skomorowski, filip pawlowski, robert moszynski, leonid rybak, liat levin, zohar amitay, j. The author investigates in detail the quantum group slqn, which is based on the classical lie group. Among the applications, studying the limit led to the discovery of crystal bases the case of. Publication date 1995 topics hopf algebras, mathematical physics, quantum groups, topology publisher new york. The continuous complexvalued functions on a compact hausdorff topological space form a commutative c. Kassel quantum groups graduate texts in mathematics 155 springer new york 1995 from math 351 at loyola university chicago. Read quantum fourier transforms and the complexity of link invariants for quantum doubles of finite groups, communications in mathematical physics on deepdyve, the largest online rental service for scholarly research with thousands of academic publications available at your fingertips.
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