Algebras of Functions on Quantum Groups: Part I by Leonid I. Korogodski PDF

By Leonid I. Korogodski

ISBN-10: 0821803360

ISBN-13: 9780821803363

The booklet is dedicated to the examine of algebras of capabilities on quantum teams. The authors' method of the topic relies at the parallels with symplectic geometry, permitting the reader to exploit geometric instinct within the idea of quantum teams. The publication contains the idea of Poisson Lie teams (quasi-classical model of algebras of capabilities on quantum groups), an outline of representations of algebras of capabilities, and the idea of quantum Weyl teams. This e-book can function a textual content for an advent to the idea of quantum teams.

Show description

Read or Download Algebras of Functions on Quantum Groups: Part I PDF

Best abstract books

Read e-book online Deformations of Algebraic Schemes PDF

This self-contained account of deformation conception in classical algebraic geometry (over an algebraically closed box) brings jointly for the 1st time a few effects formerly scattered within the literature, with proofs which are quite little recognized, but of daily relevance to algebraic geometers.

Thomas Becker's Gröbner Bases: A Computational Approach to Commutative PDF

This booklet offers a finished therapy of Gr bner bases thought embedded in an advent to commutative algebra from a computational perspective. the center-piece of Gr bner bases concept is the Buchberger set of rules, which supplies a typical generalization of the Euclidean set of rules and the Gaussian removing set of rules to multivariate polynomial earrings.

Download e-book for iPad: Combinatorial and Geometric Representation Theory by Seok-Jin Kang, Kyu-Hwan Lee

This quantity provides the complaints of the overseas convention on Combinatorial and Geometric illustration conception. within the box of illustration conception, a wide selection of mathematical rules are offering new insights, giving robust equipment for knowing the speculation, and offering a number of functions to different branches of arithmetic.

Extra info for Algebras of Functions on Quantum Groups: Part I

Sample text

Remark: The definition of cCn(p) is, of course, modelled on the way one passes from an ordinary differential equation of order n to a system of first order equations. 6. :et p be a polynomial clutching ~ n ~ (EO. E oo ). Then We have Multiplying the z on the bottom row by t gives us a homotopy between etn+1(p) and tn(p) 9 1. This establishes the first part. Similarly, o -z = a 1 -z 1 -z -z n 55. We multiply the 1 on the second row by t and obtain a homotopy between c£n+l(zp) and etn(p) Q (-z). Since -z is the composition of z with the map -1, and since -1 extends o (-1 to E, L The second @ ",..

Y is a continuous map. Vect(X) induces a ring homomorphism ~ Then f* : Vect(Y) £* : K(Y) ... K(X). :~ j if and only if E and F are stably equivalent. By ~ ~~ ~j, ;,~ (1. 4. 3) this homomorphism depends only on the homotopy class of f. (~ § Z. 2. The periodicity theorem. for K-theory is the periodicity theorem. :;~ )i 2 and K(X x S ). l cas:e of a nl01·e general theorem 'I which we shall prove. :~ - X, where X is considered to lie in E as the zero section, the non-zero complex numbers act on EO as a group of fiber preserving auto- morphisms.

It is clear that tD(p) is ~ in z. Now, define the sequence Pr(z) inductively by Then we have the following matrix identity: ... Pz 1 PI p n . 1 I Ln(p) 1 = -z 1 1 -z 1 1 or, more briefly where N I and N Z are nilpotent. is nonsingular for 0 ~ t ~ 1, PROPOSITION Z. Z. If N is nilpotent, 1 + tN so we obtain s. tn(p) ~ p G 1 ~ isomorphic bundles on P, i. e. ::!. if \k=O L k O k @EO'1'IL @E ) k=l @ EO, ,tn(p), E oo @ I k=1 O LkeE ) 54. Remark: The definition of cCn(p) is, of course, modelled on the way one passes from an ordinary differential equation of order n to a system of first order equations.

Download PDF sample

Algebras of Functions on Quantum Groups: Part I by Leonid I. Korogodski


by Robert
4.4

Rated 4.93 of 5 – based on 34 votes