2022/11/29 by Taipe, Frank
#FOS: Mathematics #Quantum Algebra (math.QA) #Rings and Algebras (math.RA)
paper · doi:10.48550/arxiv.2211.16491
In the present work, we study Yetter-Drinfeld algebras over a pairing of multiplier Hopf algebras. Our main motivation is the construction of a self-dual theory of (C*-)algebraic quantum transformation groupoids. Instead of the standard characterization of Yetter-Drinfeld algebras given in the case of Hopf algebras, we develop an equivalent "only coaction" characterization in the framework of multiplier Hopf algebras. Finally, as a special case, we focus on Yetter-Drinfeld structures over Van Daele's algebraic quantum groups.