Planar Algebras in Braided Tensor Categories (1392) (Memoirs of the American Mathematical Society, 282, Band 1392)

Henriques Andre, Gil, James Tener und David Penneys:

ISBN 10: 1470455404 / ISBN 13: 9781470455408

Verlag: American Mathematical Society, 2023

100 Seiten; 9781470455408.3 Gewicht in Gramm: 500. Bestandsnummer des Verkäufers 1115319

Inhaltsangabe:

"We generalize Jones' planar algebras by internalising the notion to a pivotal braided tensor category C. To formulate the notion, the planar tangles are now equipped with additional 'anchor lines' which connect the inner circles to the outer circle. We call the resulting notion an anchored planar algebra. If we restrict to the case when C is the category of vector spaces, then we recover the usual notion of a planar algebra. Building on our previous work on categorified traces, we prove that there is anequivalence of categories between anchored planar algebras in C and pivotal module tensor categories over C equipped with a chosen self-dual generator. Even in the case of usual planar algebras, the precise formulation of this theorem, as an equivalence of categories, has not appeared in the literature. Using our theorem, we describe many examples of anchored planar algebras"--

Über die Autorin bzw. den Autor: Andre Gil Henriques, University of Oxford, United Kingdom.

David Penneys, The Ohio State University, Columbus, Ohio.

James E. Tener, Australian National University, Canberra, Australia.

Bibliografische Details

Titel: Planar Algebras in Braided Tensor Categories...
Verlag: American Mathematical Society
Erscheinungsdatum: 2023
Einband: paperback
Zustand: Gut