We generalise the two-sided construction of examples of pairs ofsubfactors of the hyperfinite II$_1$ factor $R$ in [E1]---which ariseby considering unitary braid representations with certainproperties---to multi-sided pairs. We show that the index for themulti-sided pair can be expressed as a power of that for thetwo-sided pair. This construction can be applied to the naturalexamples---where the braid representations are obtained in connectionwith the representation theory of Lie algebras of types $A$, $B$, $C$,$D$. We also compute the (first) relative commutants.
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机译：我们将[E1]中超有限的II $ _1 $因子$ R $的子因子对的示例的双面构造概括为多对对，这是通过考虑具有某些属性的unit合编织表示而产生的。我们表明，多面对的索引可以表示为双面对的指数的幂。这种构造可以应用于自然的例子，其中辫子表示是与类型为$ A $，$ B $，$ C $，$ D $的李代数的表示理论有关的。我们还计算（第一个）相对换向器。
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