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# Multi-Sided Braid Type Subfactors

Published:2001-06-01
Printed: Jun 2001
• Juliana Erlijman
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## Abstract

We generalise the two-sided construction of examples of pairs of subfactors of the hyperfinite II$_1$ factor $R$ in [E1]---which arise by considering unitary braid representations with certain properties---to multi-sided pairs. We show that the index for the multi-sided pair can be expressed as a power of that for the two-sided pair. This construction can be applied to the natural examples---where the braid representations are obtained in connection with the representation theory of Lie algebras of types $A$, $B$, $C$, $D$. We also compute the (first) relative commutants.
 MSC Classifications: 46L37 - Subfactors and their classification

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