New Turaev braided group categories and group Schur-Weyl duality. (Q1942031)

Let \(G\) be a group. The author defines the notion of a Yetter-Drinfeld category for a crossed Turaev \(G\)-algebra, and this is shown to be a Turaev braided \(G\)-category. Long dimodule categories are introduced for \(G\)-triangular Turaev \(G\)-algebras and \(G\)-cotriangular Turaev \(G\)-algebras, and such a Long dimodule category is shown to be a symmetric Turaev braided \(G\)-category. A \(G\)-Schur-Weyl duality is obtained between a certain Turaev \(G\)-algebra and the group algebra of a symmetric group.