In general, a quantum group is some kind of hopf algebra. The theory of quantum groups has led to a new, extremely rigid structure, in which the objects of the theory are provided with. Quantum groups graduate texts in mathematics 155 by. Kassel, quantum groups, graduate texts in mathematics 155. 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. Fundamental isomorphism theorems for quantum groups request pdf. Springer made a bunch of books available for free, these were. It also produces representation theoretic structures that arise in many elds of mathematics. Drinfeldjimbos quantum enveloping algebra u qsl2, duality with the quantum algebra of functions sl. Hopf algebras, quantum groups and topological eld theory. Saieswari amaran, ronnie kosloff, michal tomza, wojciech skomorowski, filip pawlowski, robert moszynski, leonid rybak, liat levin, zohar amitay, j. Quantum groups and knot invariants christian, rosso. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent fundamental contributions.
In this book we take the analytic point of view, meaning that we work with algebras. 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. Lectures on quantum groups jens carsten jantzen download. Introduction, historical survey, hopf algebras, basic. It presents the quantum groups attached to sl2 as well as the basic concepts of the theory of hopf algebras. Publication date 1995 topics hopf algebras, mathematical physics, quantum groups, topology publisher new york. By pierre vogel, in which he extended the tate cohomology to any group. Pdf introduction to quantum groups download full pdf book.
Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. The successes of quantum mechanics have been extraordinary. 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. We also provide the most important examples, including the classi. This is an analogue to the picture for usual homological algebra, where one has the quantum general linear group 9 and the di.
The development of quantum mechanics has taken physics in a vastly new direction from that of classical physics from the very start. Quantum groups have given many examples of noncommutative noncocommutative bialgebras than were known before this research area had taken off. This thesis is brought to you for free and open access by the student. The author also discusses the quantum plane as an object that generalizes the affine plane, namely the two variables x, y generating the plane no longer commute but instead satisfy yx q xy. Quantum groups also describe symmetries in a variety of integrable systems, including in particular sectors of yangmills theories. Majid foundations of quantum group theory is an option, i havent read it. We give an elementary introduction to the theory of algebraic and topological quantum groups in the spirit of s. Kassel, quantum groups, graduate texts in mathematics.
It also produces representation theoretic structures that. The quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof. 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. Pdfepub high quality, no missing contents and printable compatible devices.
Fundamental isomorphism theorems for quantum groups. Concerning the books let me be the second one on the christian kassels book it is. 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. We also consider quantum slqngroups and quantum lorentz groups. Springer made a bunch of books available for free, these were the direct links springer free mathsbooks. A quantum dynamical study using thermal random phase wavefunctions. Hopf algebras, quantum groups and topological field theory. Reutenauer, algebraicity of the zeta function associated to a matrix over a free group algebra, arxiv. Tensor product question in kassel s quantum groups. 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. Reference for quantum groups mathematics stack exchange.
Featured on meta meta escalationresponse process update marchapril 2020 test results, next. 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. The phrase quantum jump or quantum leap is now in common usage, and incorrectly too. Turaev was a professor at the university of strasbourg and then became a professor at indiana university. They are often referred to as the free unitary and orthogonal quantum groups, respectively. 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. 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. Quantum groups graduate texts in mathematics christian kassel on. Quantum groups and their primitive ideals modern surveys in mathematics 29 by anthony joseph. To this end we establish an explicit formula for the number c n q of ideals of codimension n of the algebra. 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.
Springer made a bunch of books available for free, these were the direct links springerfreemathsbooks. Request pdf fundamental isomorphism theorems for quantum groups the lattice of subgroups of a group is the subject of numerous results revolving around the central theme of decomposing the. 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. 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. Indeed, since omnk is generated as a free algebra by the elements xij 1.
Vladimir georgievich turaev, born in 1954 is a russian mathematician, specializing in topology turaev received in 1979 from the steklov institute of mathematics his candidate of sciences degree phd under oleg viro. We also provide the most important examples, including the classification of quantum sl2. Since then quantum group theory has developed in several directions and by now there is probably no single expert who has a. The theory of quantum groups is a rapidly developing area with numerous applications in mathematics and theoretical physics, e. Femtosecond twophoton photoassociation of hot magnesium atoms. An introduction to quantum groups lectures at ncgoa07 christian. The center of quantum group can be described by quantum determinant. Pdf quantum groups download full pdf book download. Browse other questions tagged hopfalgebras quantumgroups or ask your own question.
Quantum groups and differential forms swapneel mahajan abstract. At the writing of this thesis the theory of quantum groups is a young and burgeoning. Buy quantum groups graduate texts in mathematics 155 on. Quantum groups are noncommutative algebras depending on a parameter q. An introduction to the theory of quantum groups ewu digital. An introduction to quantum groups lectures at ncgoa07 christian kassel summary lecture 1. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be used as a textbook. Lusztigs book has a reputation of being tough to read. Jantzen lectures on quantum groups is nicely written and clear, its my favourite. We define for n 2 the braid group b2 as the free group with one generator and. Since large parts of the book are independent of the theory of perverse sheaves, the work may also be. Electromagnetism and relativity, the origin of quantum physics, hamiltons variational principle and the hamilton jacobi eq, wavepackets, quantum behavior of particles, the amplitude probability, the.
Pdf introduction to quantum groups download full pdf. Springer made a bunch of books available for free, these. In fact, there continue at present to be many developments in the subject of a very fundamental nature, such as implications for the foundations of physics, physics of entanglement, geometric phases, gravity and. 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. 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. Quantum groups available for download and read online in other formats. We compute the hochschild homology of the free orthogonal quantum group aon. We compute the zeta function of the hilbert scheme of n points on a twodimensional torus and show it satisfies a remarkable functional equation.
Quantum teleportation, contrasting the classical and quantum mechanics descriptions, classical physics. Quantum groups and knot invariants pdf free download epdf. Quantum groups graduate texts in mathematics 155 by christian kassel. Cohomological invariant for groups coming from quantum group theory. 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. Drinfelds original icm86 talk quantum groups is something must read, scanned. In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebras with additional structure. At the same time this quantum group can be interpreted as the quantisation of a particle moving in a curved geometry with blackholelike features. Quantum groups and knot invariants christian, rosso, marc, turaev, vladimir kassel download bok. Introduction to quantum mechanics pdf download book. Having glanced a little bit at the last two in this list, i found both of them more difficult to read.
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