Doublecrossed Products of Quantum Groups

Lars Tuset
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Lars Tuset: Oslo Metropolitan University, Department of Computer Science

Chapter Chapter 19 in Analysis and Quantum Groups, 2022, pp 521-537 from Springer

Abstract: Abstract Given a coaction α of a locally compact quantum group (W, Δ), we establish a biduality theorem for faithful semifinite normal weights on U. Given such a weight y we talk about its Radon-Nikodym derivative (Dyα : Dy)t under α. This is an element u t ∈ W ⊗ ̄ U $$u_t\in W\bar \otimes U$$ that satisfies the following cocycle type of identity ( Δ ⊗ ι)(ut) = (ι ⊗ α)(ut)(1 ⊗ ut), and is by definition the cocycle derivative of the bidual weight of y with respect to Tr Δ x ̂ ⊗ y $$\mathrm {Tr}_{\Delta _{\hat {x}}}\otimes y$$ .

Date: 2022
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DOI: 10.1007/978-3-031-07246-8_19

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