3 edition of **On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation** found in the catalog.

On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation

Peter Schauenburg

- 376 Want to read
- 16 Currently reading

Published
**1992**
by R. Fischer in München
.

Written in English

- Yang-Baxter equation.,
- Hopf algebras.,
- Mathematical physics.

**Edition Notes**

Includes bibliographical references (p. 75-76).

Statement | Peter Schauenburg. |

Series | Algebra Berichte ;, 67 |

Classifications | |
---|---|

LC Classifications | QC174.52.Y36 S33 1992 |

The Physical Object | |

Pagination | 76 p. : |

Number of Pages | 76 |

ID Numbers | |

Open Library | OL1475455M |

ISBN 10 | 3889271014 |

LC Control Number | 93139882 |

A Lie algebra is a Hom–Lie algebra with α = –Lie algebras were introduced in [] (without multiplicativity) to describe the structures on certain q-deformations of the Witt and the Virasoro r precursors of Hom–Lie algebras can be found in [11, 14].Other classes of Hom–Lie algebras were constructed in [17, 27].We will describe some of these Hom–Lie algebras in. Hopf algebras, quantum groups and topological eld theory Winter term /20 Christoph Schweigert This is a complicated set of non-linear equations, called the Yang-Baxter equation. In this lecture, we will see how to nd solutions to this equation (and why this is an interesting.

Hopf Algebras and Quantum Groups - CRC Press Book This volume is based on the proceedings of the Hopf-Algebras and Quantum Groups conference at the Free University of Brussels, Belgium. It presents state-of-the-art papers - selected from over 65 participants representing nearly 20 countries and more than 45 lectures - on the theory of Hopf algebras. associative algebra defined a canonical solution of the quantum Yang-Baxter equation. It is known that a Hopf algebra over a commutative ring Pic K s 1, which is a finitely generated projective module, is a Frobenius algebra Therefore we can apply this construction wx. to such Hopf algebras. We obtain an explicit formula.

Request PDF | Quantum algebras, quantum coalgebras, invariants of tangles and knots | Quantum coalgebras are defined and studied. A theory of associated invariants of tangles, knots and. General form of the parameter-dependent Yang–Baxter equation. Let be a unital associative its most general form, the parameter-dependent Yang–Baxter equation is an equation for (, ′), a parameter-dependent element of the tensor product ⊗ (here, and ′ are the parameters, which usually range over the real numbers ℝ in the case of an additive parameter, or over positive.

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Abstract: Let a be a given finite-dimensional simple Lie algebra over C with a fixed invariant inner product. According to [1], the function r(u) = u −1 I μ ⊗ I μ, where {I μ} is an orthonormal basis in a (summation over repeated indices is always assumed to be carried out), satisfies the classical Yang-Baxter equation (CYBE).If, in addition, a representation ρ: a → End V is given.

Published: January (This book is a printed edition of the Special Issue Hopf Algebras, Quantum Groups and Yang-Baxter Equations that was published in Axioms). consists of pointed Hopf algebras. We note the quantized enveloping algebras described elsewhere are pointed Hopf algebras.

Thus for many reasons bialgebras are objects of fundamental interest in the study of quantum Yang-Baxter equation and quantum groups. Chapter2 The discussion of the quantum Yang-Baxter equation begins here. Additional Physical Format: Online version: Schauenburg, Peter.

On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation. München: R. Fischer, © The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Thus for many reasons pointed bialgebras are elsewhere are pointed of fundamental interest in the study of the quantum Yang-Baxter equation and objects quantum.

Preface to ”Hopf Algebras, Quantum Groups and Yang-Baxter Equations” Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are.

Chapter 1 The algebraic prerequisites for the book are covered here and in the appendix. This chapter should be used as reference material and should be consulted as needed. A systematic treatment of algebras, coalgebras, bialgebras, Hopf algebras, and represen tations of these objects to the extent needed for the book is given.

The material here not specifically cited can be found for the. We have found pointed bialgebras useful in connection with solving the quantum Yang-Baxter equation.

For this reason we develop their theory in some detail. The class of examples described in Chapter 6 in connection with the quantum double consists of pointed Hopf algebras. We note the quantized enveloping algebras described Hopf algebras. Basic properties and applications of Hopf algebras and Yang-Baxter equations are reviewed, with the quantum group U q (sl 2) as a frequent example.

The development builds up to the representation theory of quasitriangular Hopf algebras. Much of the abstract representation theory is new, including a formula for the rank of a representation.

Quantum algebras and coalgebras account for regular isotopy invariants of un- in the same ways that quantum algebras and oriented quantum algebras are. Coquasitriangular Hopf algebras have a quantum coalgebra structure. There the quantum Yang–Baxter and braid equations.

In our special issues on Hopf algebras, quantum groups and Yang-Baxter equations, several papers [8][9][10][11][12][13][14][15][16][17], as well the feature paper [18], covered many topics related.

The Cylinder Product and Cylinder Matrices On Coquasitriangular Hopf Algebras and the Quantum Yang–Baxter Equation, Algebra Berichte, 67, Fischer, Munich () Google Scholar. TakeuchiMatric bialgebras and quantum groups. Israel J. Math., 72 (), pp.

Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita (ed.). Publisher: MDPI AG ISBN Number of pages: Description: Various aspects of the Yang-Baxter equation, related algebraic structures, and applications are presented in this volume.

Free 2-day shipping. Buy Hopf Algebras, Quantum Groups and Yang-Baxter Equations (Paperback) at Schauenburg P On coquasitriangular Hopf algebras and the quantum Yang-Baxter equation Algebra Berichte vol 67 ed R Fischer (München: Verlag) [23] Sweedler M Hopf Algebras.

Home > Hopf algebras and the quantum Yang-Baxter equation Information ; References (0) Citations () Files ; Plots.

Hopf algebras and the quantum Yang-Baxter equation. V.G. Drinfeld (Kharkov, Inst. Low Temp. Phys.) - 5 pages 32 () () ; Record addedlast. Hopf Algebras, Quantum Groups and Yang-Baxter Equations by Florin Felix Nichita (ed.) Publisher: MDPI AG ISBN Number of pages:.

Get this from a library. Introduction to the quantum Yang-Baxter equation and quantum groups: an algebraic approach. [Larry A Lambe; David E Radford] -- The quantum Yang-Baxter equation is an important equation to solve for applications in physics and topology. This book treats the equation in the context of algebraic systems and as a problem for.

14 Coquasitriangular bialgebras and Hopf algebras Coquasitriangular and Yang-Baxter coalgebras Coquasitriangular bialgebras and Hopf algebras The square of the antipode of a coquasitriangular Hopf algebra The free coquasitriangular bialgebra on a coquasitriangular coalgebra 15 Pointed Hopf algebras Pages: M.

TakeuchiThe coquasitriangular Hopf algebra associated with a rigid Yang–Baxter coalgebra S. Caenepeel (Ed.), Proc. Coll. Hopf Algebras and Quantum Groups, Dekker, Brussels (), pp. Google Scholar. It presents the quantum groups attached to SL2 as well as the basic concepts of the theory of Hopf algebras.

Coverage also focuses on Hopf algebras that produce solutions of the Yang-Baxter equation and provides an account of Drinfeld's elegant treatment of the monodromy of the Knizhnik-Zamolodchikov s: 3.hopf algebras quantum groups and yang baxter equations Download hopf algebras quantum groups and yang baxter equations or read online books in PDF, EPUB, Tuebl, and Mobi Format.

Click Download or Read Online button to get hopf algebras quantum groups and yang baxter equations book now. This site is like a library, Use search box in the widget.Sections 2–6, is devoted to the basics of Hopf algebra theory and examples, in ascending level of complexity.

Part II turns around the all-important Faa di Bruno Hopf algebra. Section 7 contains a ﬁrst, direct approach to it. Section 8 gives applications of the Faa di Bruno algebra to quantum ﬁeld theory and Lagrange reversion.

Section 9.