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Pontryagin Duality for a Class of Locally Compact Quantum Groups
Author(s) -
Hollevoet Jan
Publication year - 1995
Publication title -
mathematische nachrichten
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.913
H-Index - 50
eISSN - 1522-2616
pISSN - 0025-584X
DOI - 10.1002/mana.19951760108
Subject(s) - mathematics , pontryagin's minimum principle , locally compact space , duality (order theory) , pure mathematics , crossed product , quantum , heisenberg group , product (mathematics) , class (philosophy) , space (punctuation) , algebra over a field , quantum mechanics , physics , optimal control , geometry , mathematical optimization , linguistics , philosophy , artificial intelligence , computer science
A class of locally compact quantum semigroups in the sense of WORONOWICZ , containing the quantized Heisenberg group, is studied. The underlying quantum space is described in terms of a crossed product. We show the existence of a universal corepresentation and a Pontryagin dual, which turns out to be a twisted crossed product. The Pontryagin duality for these quantum semigroups is investigated.