Introduction, historical survey, hopf algebras, basic. Hopf algebras, quantum groups and yangbaxter equations mdpi. Pdf some introductory notes on quantum groups, quantum. Commons attribution cc by license, which allows users to download, copy and build. Kassel has numerous publications, including the book quantum groups in the springer gradate texts in mathematics series. An introduction to quantum computing for nonphysicists. Quantum groups quantized enveloping algebras and related deformations see also 16t20, 20g42, 81r50, 82b23 81r50. Cyclic groups and quantum logic gates pdf free download. Pdf introduction to quantum groups download full pdf. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with. Pdf quantum groups download full pdf book download. Between 1987 and 1995 literally thousands of papers on quantum groups have been published.
Download quantum computation and quantum information pdf. Hopf algebras and polynomial identities quantum groups and. The classical description of a particle, hilbert space formalism, group theory, lie algebra, the green function approach, the evolution operator, scattering theory, quantum mechanics in. Abstract let r be an integral domain, let 2 r n f0g be such that. International journal of mathematics and mathematical sciences. When dxtasheet select the in this file command, acrobat will run an optical character recognition process that will convert the image to selectable text and then this will allow you to copy the text in the document.
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. 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. By choosing representations of the braid groups, one obtains numerical or matrix. An introduction to quantum groups lectures at ncgoa07 christian kassel summary lecture 1. Drinfeld, quantum groups, in proceedings of the international congress of mathematicians, a.
Building qubits phase across junction energy maximum 0 energy energy minimum energy diagram of a junction electrons weak link superconductor what are the basic principles. 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. In fact, chemists, who have used nmr for decades to study complicated molecules, have been doing quantum computing. An introduction to quantum groups lectures at ncgoa07 christian. Introduction to quantum mechanics pdf download book. 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. We describe the use of a single quantum bit for secure key distribution. Christian kassel is the author of quantum groups 3. Drinfeldjimbos quantum enveloping algebra u qsl2, duality with the quantum algebra of functions sl. Lectures on quantum groups jens carsten jantzen download.
Quantum groups and representations of monoidal categories. We study the dynamical analogue of the matrix algebra m n, constructed from a dynamical rmatrix given by etingof and varchenko. There are two directories included for the 32bit and the 64bit version, respectively. Download fulltext pdf some introductory notes on quantum groups, quantum algebras, and their applications article pdf available june 2001 with 27 reads. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with knot theory and drinfelds recent fundamental contributions. As i discuss in this introcjuctory section, the equations that govern the motions of electrons and of nuclei are not the familiar newton equatrons. Someone who acts and reads a lot will see and know. 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. But the real power of quantum computation derives from the exponential state spaces of multiple quantum bits. The center of quantum group can be described by quantum determinant.
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. Jimbo, independently, in their study of the quantum yangbaxter equation arising from 2dimensional solvable lattice models. This book provides an introduction to the theory of quantum groups with emphasis. 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. It presents the quantum groups attached to sl2 as well as the basic concepts of the theory of hopf algebras. Even single quantum bits enable interesting applications. 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. At the same time this quantum group can be interpreted as the quantisation of a particle moving in a curved geometry with blackholelike features. More precisely, for every pairi, nof natural numbers, there is defined an elementb n i of the braid group algebrakb n, and these satisfy analogs of the classical identities for the binomial coefficients. Monoidal bicategories and hopf algebroids sciencedirect. Quantum groups have given many examples of noncommutative noncocommutative bialgebras than were known before this research area had taken off.
Mathematical society of japan memoirs project euclid. Fundamental isomorphism theorems for quantum groups. Quantum computing with molecules scientific american june 1998 67 conventional electronic computers will soon face fundamental limits to their per formance, but quantum computers, based on the molecules in a liquid held in a magnetic. The dllfile needs to be in the same directory as the exefile, when running the program.
Quantum groups and knot invariants prasolov, sossinsky. If youre looking for a free download links of quantum computation and quantum information pdf, epub, docx and torrent then this site is not for you. The classical identities between theqbinomial coefficients and factorials can be generalized to a context in which numbers are replaced by braids. This paper is intended to make explicit some aspects of the interactions which have recently come to light between the theory of classical knots and links, the theory of monoidal categories, hopfalgebra theory, quantum integrable systems, the theory of exactly solvable models in statistical mechanics, and quantum field theories. Hopf algebras, quantum groups and topological eld theory winter term 201920. 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.
Braids,qbinomials, and quantum groups sciencedirect. The classical description of a particle, hilbert space formalism, group theory, lie algebra, the green function approach, the evolution operator, scattering theory, quantum mechanics in practice, dynamics and driven systems. From coalgebras to drinfeld algebras steven shnider, shlomo sternberg download bok. At the writing of this thesis the theory of quantum groups is a young and. Hopf algebras, quantum groups and topological eld theory. Features and benefits access from any pc or mobile device intuitive design simple operation provides actionable information that improves the performance of your building introducing quantum vue quantum vue is a new, easytouse facility management tool that provides fullsystem monitoring of electric light and daylight from any device. Quantum logic gates and nuclear magnetic resonance pulse sequences nmr quantum logic gates for homonuclear spin systems singleflux quantum logic circuits exploiting collisionbased fusion gates. By choosing representations of the braid groups, one obtains numerical or matrix realizations of these identities.
The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer. Graduate texts in mathematics 155, springer, berlin, 1995. There is an underlying, more general theory of which wave mechanics is but one mathematical manifestation or representation. We call h 2 ha a quantized function algebra qfa, resp. Having glanced a little bit at the last two in this list, i found both of them more difficult to read. 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.
The phrase quantum jump or quantum leap is now in common usage, and incorrectly too. An introduction to the theory of quantum groups ewu digital. Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. Pdf introduction to quantum groups download full pdf book. Hopf algebras, quantum groups and topological field theory. Zero state epub book download, pdf download, read pdf, download pdf, kindle download pdf quantum break.
Quantum groups available for download and read online in other formats. By representing each qubit with a vast collection of mol ecules, one can afford to let measurements interact with a few of them. Hopf algebras and polynomial identities quantum groups and quantum topology by christian kassel. The quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof. Quantum logic gates and nuclear magnetic resonance pulse sequences nmr quantum logic gates for homonuclear spin systems singlefluxquantum logic circuits exploiting collisionbased fusion gates. Turaev, ribbon graphs and their invariants derived from quantum groups, comm. Quantum groups are certain families of hopf algebras that are deformations of universal enveloping algebras of kacmoody algebras. Quantum groups kassel pdf preliminaries christian kassel download pdf 1558kb.
The successes of quantum mechanics have been extraordinary. Qalgebroids and their cohomology mehta, rajan amit, journal of symplectic geometry, 2009. A left and a right corepresentation of this algebra, which can be seen as analogues of the exterior algebra representation, are defined and this defines dynamical quantum minor determinants as the matrix elements of these corepresentations. Fundamental isomorphism theorems for quantum groups request pdf. 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. Hopf algebras and polynomial identities quantum groups and quantum topology by christian kassel download pdf 2 mb. Download quantum computation and quantum information pdf ebook. Vladimir turaev was also a professor at the cnrs and is currently at indiana university in the department of mathematics.
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