- deformation2.pdf (438k)

## Forfatter(e)

## Utgivelsesdato

2014-01-15

## Utgiver

Elsevier

## Dokumenttype

## Sammendrag

Given a C
∗
-algebra
A
with a left action of a locally compact
quantum group
G
on it and a unitary 2-cocycle
Ω
on
ˆ
G
,we
define a deformation
A
Ω
of
A
. The construction behaves well
under certain additional technical assumptions on
Ω
,themost
important of which is regularity, meaning that
C
0
(
G
)
Ω
G
is isomorphic to the algebra of compact operators on some
Hilbert space. In particular, then
A
Ω
is stably isomorphic to
the iterated twisted crossed product
ˆ
G
op
Ω
G
A
. Also, in
good situations, the C
∗
-algebra
A
Ω
carries a left action of the
deformed quantum group
G
Ω
andwehaveanisomorphism
G
Ω
A
Ω
∼
=
G
A
.When
G
is a genuine locally compact
group, we show that the action of
G
on
C
0
(
G
)
Ω
=
C
∗
r
(
ˆ
G
;
Ω
)
is always integrable. Stronger assumptions of properness and
saturation of the action imply regularity. As an example, we
make a preliminary analysis of the cocycles on the duals of
some solvable Lie groups recently constructed by Bieliavsky
et al., and discuss the relation of our construction to that of
Bieliavsky and Gayral.

## Versjon

acceptedVersion

## Permanent URL

- http://hdl.handle.net/10642/4640