2006/04/28 by P. M. Sołtan, Piotr Mikołaj Sołtan
Mathematics · #Advanced Operator Algebra Research #Algebra over a field #Algebraic structures and combinatorial models #Compact quantum group #Compactification (mathematics) #Holomorphic and Operator Theory #Homomorphism #Hopf algebra #Locally compact space #Multiplier (economics) #Quantum group #Unital #math.QA #msc:16S10 #msc:16W30 #msc:20G42
paper · pdf · doi:10.1007/s10468-006-9035-0
published as Alg. Rep. Th. Vol. 9 No. 6 (2006) 581-591
arxiv created 2006/04/28 · openalex publication_date 2006/08/15 · openalex created_date 2016/06/24 · arxiv updated 2016/08/14 · openalex updated_date 2026/08/05
Given a discrete quantum group A we construct a certain Hopf *-algebra AP which is a unital *-subalgebra of the multiplier algebra of A. The structure maps for AP are inherited from M(A) and thus the construction yields a compactification of A which is analogous to the Bohr compactification of a locally compact group. This algebra has the expected universal property with respect to homomorphisms from multiplier Hopf algebras of compact type (and is therefore unique). This provides an easy proof of the fact that for a discrete quantum group with an infinite dimensional algebra the multiplier algebra is never a Hopf algebra.