Compactifications of discrete quantum groups

Details Compactifications of discrete quantum groups Compactifications of discrete quantum groups

2006-04-28

arxiv.org/abs/math/0604618v1

Alg. Rep. Th. Vol. 9 No. 6 (2006) 581-591

Mathematics

Quantum Algebra

Scientific paper

10.1007/s10468-006-9035-0

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.

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