Transmutation and Bosonisation of Quasi-Hopf Algebras

2009/03/24 by Klim, J
#FOS: Mathematics #FOS: Physical sciences #Mathematical Physics (math-ph) #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)

paper · doi:10.48550/arxiv.0903.3959

Abstract

Let H be a quasitriangular quasi-Hopf algebra, we construct a braided group \underlineH in the quasiassociative category of left H-modules. Conversely, given any braided group B in this category, we construct a quasi-Hopf algebra B\rtimes H in the category of vector spaces. We generalise the transmutation and bosonisation theory of [10] to the quasi case. As examples, we bosonise the octonion algebra to an asoociative one, obtain the twisted quantum double D^ϕ(G) of a finite group as a bosonisation, and obtain its transmutation. Finally, we show that \underlineH\rtimes H is isomorphic to H_\Rcal\blackbowtie H as quasi-Hopf algebras.

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