Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras

Details Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras

2000-09-14

arxiv.org/abs/math/0009141v1

Mathematics

Quantum Algebra

22 pg, latex

Scientific paper

The study of the pentagon (fusion) equation leds to the Structure and the Classification theorem for finite dimenasional Hopf algebras: there exists a one to one correspondence between the set of types of n-dimensional Hopf algebtras and the set of the orbits of the resticted Jordan action $GL_n(k) \times M_n(k)\otimes M_n(k) \to M_n(k) \otimes M_nk$ $(u, R) \to (u\otimes u)R (u\otimes u)^{-1}$, the representatives of wich are invertible solutions of length n of the pentagon equation.

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