Hopf algebras, quantum groups and topological field theory. Hopf algebras and polynomial identities quantum groups and quantum topology by christian kassel. 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. 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. Between 1987 and 1995 literally thousands of papers on quantum groups have been published.
Quantum logic gates and nuclear magnetic resonance pulse sequences nmr quantum logic gates for homonuclear spin systems singlefluxquantum logic circuits exploiting collisionbased fusion gates. 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. Qalgebroids and their cohomology mehta, rajan amit, journal of symplectic geometry, 2009. 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. By representing each qubit with a vast collection of mol ecules, one can afford to let measurements interact with a few of them. Quantum groups available for download and read online in other formats. Drinfeld, quantum groups, in proceedings of the international congress of mathematicians, a. 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.
At the same time this quantum group can be interpreted as the quantisation of a particle moving in a curved geometry with blackholelike features. Introduction, historical survey, hopf algebras, basic examples, algebra of regular functions on sl2. The josephson junction is the basic building block of a superconducting qubit, and thus a quantum computer. Lectures on quantum groups jens carsten jantzen download.
Download fulltext pdf some introductory notes on quantum groups, quantum algebras, and their applications article pdf available june 2001 with 27 reads. From coalgebras to drinfeld algebras steven shnider, shlomo sternberg download bok. This book provides an introduction to the theory of quantum groups with emphasis. There are two directories included for the 32bit and the 64bit version, respectively. Introduction, historical survey, hopf algebras, basic. Having glanced a little bit at the last two in this list, i found both of them more difficult to read. The quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof.
Quantum groups and representations of monoidal categories. 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. Download quantum computation and quantum information pdf. By choosing representations of the braid groups, one obtains numerical or matrix. Commons attribution cc by license, which allows users to download, copy and build. Hopf algebras, quantum groups and topological eld theory winter term 201920. Fundamental isomorphism theorems for quantum groups request pdf. It presents the quantum groups attached to sl2 as well as the basic concepts of the theory of hopf algebras. At the writing of this thesis the theory of quantum groups is a young and.
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. The dllfile needs to be in the same directory as the exefile, when running the program. Pdf quantum groups download full pdf book download. The classical identities between theqbinomial coefficients and factorials can be generalized to a context in which numbers are replaced by braids. 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. 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. But the real power of quantum computation derives from the exponential state spaces of multiple quantum bits. As i discuss in this introcjuctory section, the equations that govern the motions of electrons and of nuclei are not the familiar newton equatrons. There is an underlying, more general theory of which wave mechanics is but one mathematical manifestation or representation.
An introduction to quantum groups lectures at ncgoa07 christian. Monoidal bicategories and hopf algebroids sciencedirect. Abstract let r be an integral domain, let 2 r n f0g be such that. 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. Vladimir turaev was also a professor at the cnrs and is currently at indiana university in the department of mathematics. 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. Here is an introduction to the theory of quantum groups with emphasis on the spectacular connections with.
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. Mathematical society of japan memoirs project euclid. In fact, chemists, who have used nmr for decades to study complicated molecules, have been doing quantum computing. By choosing representations of the braid groups, one obtains numerical or matrix realizations of these identities. Christian kassel is the author of quantum groups 3. Fundamental isomorphism theorems for quantum groups. Pdf introduction to quantum groups download full pdf 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 call h 2 ha a quantized function algebra qfa, resp. Quantum groups kassel pdf preliminaries christian kassel download pdf 1558kb. 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.
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. 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. Pdf some introductory notes on quantum groups, quantum. The phrase quantum jump or quantum leap is now in common usage, and incorrectly too.
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. An introduction to the theory of quantum groups ewu digital. 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. Graduate texts in mathematics 155, springer, berlin, 1995. Quantum groups and related algebraic methods see also 16t20, 17b37 citation. Jimbo, independently, in their study of the quantum yangbaxter equation arising from 2dimensional solvable lattice models. Pdf introduction to quantum groups download full pdf. The center of quantum group can be described by quantum determinant. Download quantum computation and quantum information pdf ebook. The successes of quantum mechanics have been extraordinary. Hopf algebras, quantum groups and yangbaxter equations mdpi. Zero state epub book download, pdf download, read pdf, download pdf, kindle download pdf quantum break. Turaev, ribbon graphs and their invariants derived from quantum groups, comm. We study the dynamical analogue of the matrix algebra m n, constructed from a dynamical rmatrix given by etingof and varchenko.
An introduction to quantum groups lectures at ncgoa07 christian kassel summary lecture 1. Quantum groups and knot invariants prasolov, sossinsky. Hopf algebras, quantum groups and topological eld theory. 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.
Braids,qbinomials, and quantum groups sciencedirect. Quantum groups have given many examples of noncommutative noncocommutative bialgebras than were known before this research area had taken off. 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. International journal of mathematics and mathematical sciences. Introduction to quantum mechanics pdf download book. Hopf algebras and polynomial identities quantum groups and. 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. Download now the quantum groups discussed in this book are the quantized enveloping algebras introduced by drinfeld and jimbo in 1985, or variations thereof. An introduction to quantum computing for nonphysicists.
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