We define Jones's planar algebra as a map of multicategories and construct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We introduce the concept of affine representations of a planar algebra and prove some finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.
","abstract_html":"<p>We define Jones's planar algebra as a map of multicategories and construct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We introduce the concept of affine representations of a planar algebra and prove some finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.</p>","abstract_has_math":false,"creators":["Ghosh, Shamindra Kumar"],"institution":null,"degree_name":"Doctor of Philosophy","degree_level":"Dissertation","degree_discipline":null,"degree_department":null,"school":null,"contributors":["Dmitri Nikshych"],"advisors":[],"committee_chairs":[],"committee_members":[],"year":2006,"date_issued":"2006-01-01T08:00:00Z","date_published":"2006-01-01T08:00:00Z","updated_at":"2026-07-24T05:22:19Z","subjects":["Mathematics"],"languages":[],"rights":[],"rights_urls":[],"identifier_entries":[]},"links":{"outbound_url":"https://scholars.unh.edu/dissertation/339","outbound_label":"Repository record","outbound_source":"dc:identifier"},"metadata_groups":[{"id":"people","label":"People","entries":[{"key":"dc:contributor","label":"Contributor","values":["Dmitri Nikshych"]},{"key":"dc:creator","label":"Author","values":["Ghosh, Shamindra Kumar"]}]},{"id":"academic_context","label":"Academic Context","entries":[{"key":"thesis:degree_level","label":"Degree Level","values":["Dissertation"]},{"key":"thesis:degree_name","label":"Degree Name","values":["Doctor of Philosophy"]}]},{"id":"subjects_keywords","label":"Subjects and Keywords","entries":[{"key":"dc:subject","label":"Dc Subject","values":["Mathematics"]}]},{"id":"identifiers","label":"Identifiers","entries":[{"key":"dc:identifier","label":"Identifier","values":["https://scholars.unh.edu/dissertation/339"]}]},{"id":"additional","label":"Additional Metadata","entries":[{"key":"dc:description.abstract","label":"Abstract","values":["We define Jones's planar algebra as a map of multicategories and construct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We introduce the concept of affine representations of a planar algebra and prove some finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.
"]},{"key":"dc:title","label":"Title","values":["Planar algebras: A category theoretic point of view"]}]}],"canonical_facts":{"dc:contributor":["Dmitri Nikshych"],"dc:creator":["Ghosh, Shamindra Kumar"],"dc:description.abstract":["We define Jones's planar algebra as a map of multicategories and construct a planar algebra starting from a 1-cell in a pivotal strict 2-category. We introduce the concept of affine representations of a planar algebra and prove some finiteness results for the affine representations of finite depth planar algebras. We also show that the radius of convergence of the dimension of an affine representation of the planar algebra associated to a finite depth subfactor is at least as big as the inverse-square of the modulus.
"],"dc:identifier":["https://scholars.unh.edu/dissertation/339"],"dc:subject":["Mathematics"],"dc:title":["Planar algebras: A category theoretic point of view"],"thesis:degree_level":["Dissertation"],"thesis:degree_name":["Doctor of Philosophy"]},"updated_at":"2026-07-24T05:22:19Z"}