Constructing New Braided T-Categories Over Regular Multiplier Hopf Algebras

Let A be a regular multiplier Hopf algebra, and let Aut(A) denote the set of all isomorphisms α from A to itself that are algebra maps satisfying (Δ ○ α)(a) = (α ? α) ○ Δ(a) for all a ∈ A. Let G be a certain crossed product group Aut(A) × Aut(A). The main purpose of this article is to provide a class of new braided T-categories in the sense of Turaev [citealp9]. For this, we introduce a class of new categories _A 𝒴𝒟 ^A (α, β) of (α, β)-Yetter–Drinfel'd modules with α, β ∈Aut(A), and we show that the category ?𝒴𝒟(A) = { _A 𝒴𝒟 ^A (α, β)}_{(α, β)∈G} becomes a braided T-category over G, generalizing the main constructions by Panaite and Staic [6 Panaite , F. , Staic , M. D. ( 2007 ). Generalized (anti) Yetter–Drinfel'd modules as components of a braided T-category . Israel J. Math. 158 : 349 – 365 .[Crossref], [Web of Science ®] , [Google Scholar]].