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arXiv · 1011.1808

Weights on bimodules

Paramita Das·Shamindra Kumar Ghosh
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Abstract

The concept of a {\em weight} on a planar algebra was introduced in \cite{DGG}. In this article we give an alternate characterization of weights on a planar algebra in terms of `weight functions' on the vertices of the principal graphs. Using this characterization we show that the property of bifinite bimodules of having a `trivial perturbation class' is closed under Connes fusion. We give a direct and constructive method of perturbing a bifinite bimodule by a positive weight in such a way that the bimodule planar algebra of the perturbed bimodule is isomorphic to the perturbation of the one associated to the initial bimodule by the given weight.

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Paramita Das, Shamindra Kumar Ghosh. 2010-11-08. Weights on bimodules. https://arxiv.org/abs/1011.1808

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