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Unitaires multiplicatifs en dimension finie et leurs sous-objets

Saad Baaj·Etienne Blanchard·Georges Skandalis
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Abstract

A pre-subgroup of a multiplicative unitary $V$ on a finite dimensionnal Hilbert space $H$ is a vector line $L$ in $H$ such that $V(L\otimes L)=L\otimes L$. We show that there are finitely many pre-subgroups, give a Lagrange theorem and generalize the construction of a `bi-crossed product'. Moreover, we establish bijections between pre-subgroups and coideal subalgebras of the Hopf algebra associated with $V$, and therefore with the intermediate subfactors of the associated (depth two) inclusions. Finally, we show that the pre-subgroups classify the subobjects of $(H,V)$.

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Saad Baaj, Etienne Blanchard, Georges Skandalis. 1998-04-22. Unitaires multiplicatifs en dimension finie et leurs sous-objets. https://arxiv.org/abs/math/9804104

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