Every symmetric generating functional of a convolution semigroup of states on a locally compact quantum group is shown to admit a dense unital ∗-subalgebra with core-like properties in its domain. On the other hand we prove that every normalised, symmetric, hermitian conditionally positive functional on a dense ∗-subalgebra of the unitisation of the universal C$^∗$-algebra of a locally compact quantum group, satisfying certain technical conditions, extends in a canonical way to a generating functional. Some consequences of these results are outlined, notably those related to constructing cocycles out of convolution semigroups.
|Number of pages||29|
|Journal||International Mathematics Research Notices|
|State||Published - 1 Jul 2021|
Bibliographical noteFunding Information:
This work was partially supported by the National Science Centre (NCN) [2014/14/E/ST1/00525 to A.S.].
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ASJC Scopus subject areas
- Mathematics (all)