Injectivity for algebras and categories with quantum symmetry
Lucas Hataishi, Makoto Yamashita
TL;DR
This paper proves the existence of injective envelopes for certain quantum algebra structures and explores their implications for boundary actions in quantum group categories, advancing the understanding of quantum symmetries.
Contribution
It introduces the existence of injective envelopes for unital Yetter-Drinfeld C*-algebras and related bimodule categories, revealing new invariance properties in quantum group theory.
Findings
Existence of injective envelopes for unital Yetter-Drinfeld C*-algebras
Monoidal invariance for boundary actions of Drinfeld doubles
Advancement in understanding quantum symmetries
Abstract
We establish the existence of injective envelopes for unital Yetter-Drinfeld C*-algebras, and a related class of bimodule categories over rigid C*-tensor categories. This implies monoidal invariance for boundary actions of Drinfeld doubles of compact quantum groups.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Operator Algebra Research · Homotopy and Cohomology in Algebraic Topology