English

Weights on bimodules

Quantum Algebra 2010-11-09 v1 Operator Algebras

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.

Keywords

Cite

@article{arxiv.1011.1808,
  title  = {Weights on bimodules},
  author = {Paramita Das and Shamindra Kumar Ghosh},
  journal= {arXiv preprint arXiv:1011.1808},
  year   = {2010}
}
R2 v1 2026-06-21T16:40:32.923Z