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

G. Militaru
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Abstract

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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G. Militaru. 2000-09-14. Heisenberg duoble, pentagon equation, structure and classification of finite dimensional Hopf algebras. https://doi.org/10.1112/s0024610703004897

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