2010/11/08 by Paramita Das, Das, Paramita, Shamindra Kumar Ghosh +1
Mathematics · #46L37 #Advanced Operator Algebra Research #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Operator Algebras (math.OA) #Quantum Algebra (math.QA) #math.OA #math.QA #msc:46L37
paper · pdf · doi:10.48550/arxiv.1011.1808
arxiv created 2010/11/08 · openalex publication_date 2010/11/08 · arxiv updated 2010/11/09 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
The concept of a \em weight on a planar algebra was introduced in \citeDGG. 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.