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A duality Hopf algebra for holomorphic N=1 special geometries

Karl-Georg Schlesinger
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Abstract

We find a self-dual noncommutative and noncocommutative Hopf algebra acting as a universal symmetry on the modules over inner Frobenius algebras of modular categories (as used in two dimensional boundary conformal field theory) similar to the Grothendieck-Teichmueller group GT as introduced by Drinfeld as a universal symmetry of quasitriangular quasi-Hopf algebras. We discuss the relationship to a similar self-dual, noncommutative, and noncocommutative Hopf algebra, previously found as the universal symmetry of trialgebras and three dimensional extended topological quantum field theories. As an application of our result, we get a transitive action of a sub-Hopf algebra of the latter universal symmetry algebra on the relative period matrices of holomorphic N=1 special geometries.

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Karl-Georg Schlesinger. 2004-02-04. A duality Hopf algebra for holomorphic N=1 special geometries. https://arxiv.org/abs/math/0402061

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