ترغب بنشر مسار تعليمي؟ اضغط هنا

Actions of locally compact (quantum) groups on ternary rings of operators, their crossed products and generalized Poisson boundaries

163   0   0.0 ( 0 )
 نشر من قبل Adam Skalski
 تاريخ النشر 2015
  مجال البحث
والبحث باللغة English




اسأل ChatGPT حول البحث

Actions of locally compact groups and quantum groups on W*-ternary rings of operators are discussed and related crossed products introduced. The results generalise those for von Neumann algebraic actions with proofs based mostly on passing to the linking von Neumann algebra. They are motivated by the study of fixed point spaces for convolution operators generated by contractive, non-necessarily positive measures, both in the classical and in the quantum context.



قيم البحث

اقرأ أيضاً

170 - Pekka Salmi 2012
This is a short survey on idempotent states on locally compact groups and locally compact quantum groups. The central topic is the relationship between idempotent states, subgroups and invariant C*-subalgebras. We concentrate on recent results on loc ally compact quantum groups, but begin with the classical notion of idempotent probability measure. We also consider the `intermediate case of idempotent states in the Fourier--Stieltjes algebra: this is the dual case of idempotent probability measures and so an instance of idempotent states on a locally compact quantum group.
A general form of contractive idempotent functionals on coamenable locally compact quantum groups is obtained, generalising the result of Greenleaf on contractive measures on locally compact groups. The image of a convolution operator associated to a contractive idempotent is shown to be a ternary ring of operators. As a consequence a one-to-one correspondence between contractive idempotents and a certain class of ternary rings of operators is established.
A C*-dynamical system is said to have the ideal separation property if every ideal in the corresponding crossed product arises from an invariant ideal in the C*-algebra. In this paper we characterize this property for unital C*-dynamical systems over discrete groups. To every C*-dynamical system we associate a twisted partial C*-dynamical system that encodes much of the structure of the action. This system can often be untwisted, for example when the algebra is commutative, or when the algebra is prime and a certain specific subgroup has vanishing Mackey obstruction. In this case, we obtain relatively simple necessary and sufficient conditions for the ideal separation property. A key idea is a notion of noncommutative boundary for a C*-dynamical system that generalizes Furstenbergs notion of topological boundary for a group.
205 - Nandor Sieben 2010
Morita equivalence of twisted inverse semigroup actions and discrete twisted partial actions are introduced. Morita equivalent actions have Morita equivalent crossed products.
118 - Pekka Salmi , Adam Skalski 2016
Correspondence between idempotent states and expected right-invariant subalgebras is extended to non-coamenable, non-unimodular locally compact quantum groups; in particular left convolution operators are shown to automatically preserve the right Haar weight.
التعليقات
جاري جلب التعليقات جاري جلب التعليقات
سجل دخول لتتمكن من متابعة معايير البحث التي قمت باختيارها
mircosoft-partner

هل ترغب بارسال اشعارات عن اخر التحديثات في شمرا-اكاديميا