Mathematics

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Define the planar algebra of tensors, *-structure, sphericality, subfactor planar algebra.
Correction in the definition of a tangle, planar algebras by generators and relations, the Temperley-Lieb planar algebra, finite-dimensionality, connectedness, irreducibilty and the modulus condition.
We will constrcut the planar algebra of tensors.
We define the notion of planar algebra.
We define and give examples of planar tangles in the sense of Jones. We also discuss the two operations of renumbering and composition.

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