Commutative Algebras in Braided Monoidal Categories and Rigidity

Explore a mathematical seminar talk that delves into commutative algebras within braided monoidal categories and their rigidity properties. Learn about joint research findings from collaborations with Thomas Creutzig, Kenichi Shimizu, Harshit Yadav, and Jinwei Yang, focusing on conditions under which categories of modules inherit rigidity properties. Examine how these theoretical frameworks apply to vertex operator algebras (VOAs) and their extensions, particularly in cases involving finite braided tensor categories and Grothendieck-Verdier categories. Discover applications to simple non-negative integer-graded VOAs and their relationships with strongly rational vertex operator subalgebras, as well as implications for weight modules in simple affine VOAs of sl_2 at admissible levels. The presentation includes detailed mathematical proofs and references to recent research published on arXiv, offering insights into advanced concepts in quantum algebra and category theory.