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By Enriquez B. (ed.)

ISBN-10: 3037190477

ISBN-13: 9783037190470

The quantity begins with a lecture direction via P. Etingof on tensor different types (notes via D. Calaque). This path is an advent to tensor different types, resulting in subject matters of contemporary study equivalent to realizability of fusion earrings, Ocneanu stress, module different types, vulnerable Hopf algebras, Morita conception for tensor different types, lifting concept, express dimensions, Frobenius-Perron dimensions, and the type of tensor different types. the rest of the ebook includes 3 unique expositions on associators and the Vassiliev invariants of knots, classical and quantum integrable structures and elliptic algebras, and the teams of algebra automorphisms of quantum teams. The preface places the consequences offered in point of view. Directed at examine mathematicians and theoretical physicists in addition to graduate scholars, the quantity offers an outline of the continuing study within the area of quantum teams, a major topic of present mathematical physics.

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Linear weight systems . . . . . 7 The Kontsevich integral of unitrivalent graphs . 8 The Alexander series of a tetrahedron . . . 1j1/-modules . . . . 10 Proof of Theorem 1 . . . . . . . . y and Viro’s Alexander invariant . . . . 11 r References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

DimC /ıij : k Thus if p C is a modular category, then dim C ¤ 0 and we can define new numbers sij D Sij = dim C (here we must make a choice of the square root). 18 (Verlinde formula, [BaKi]). X sir sjr Nij˛ s˛r D : s0r ˛ So sir =s0r are eigenvalues of the multiplication matrix Ni . , roots of a monic polynomial with integer coefficients - the characteristic polynomial of Ni ). 19. dim Xr /2 D si r si 2 s0r r is an algebraic integer. This result will be very useful to prove classification theorems in Section 4.

B] J. Bichon, The representation category of the quantum group of a non-degenerate bilinear form, Comm. Algebra 31 (2003), 4931–4851. [BW] E. Blanchard, A. Wassermann, in preparation. [BNS] G. Böhm, F. Nill, K. Szlachányi, Weak Hopf algebras I. Integral theory and C -structure, J. Algebra 221 (1999), 357–375. [Ca] J. W. Cassels, Local fields, London Math. Soc. Stud. Texts 3, Cambridge University Press, Cambridge 1986. [CG] A. Coste, T. Gannon, Remarks on Galois symmetry in rational conformal field theories, Phys.

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Quantum groups by Enriquez B. (ed.)

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