[PDF] Top 20 Around Property (T) for Quantum Groups

... of Property (T), which can be roughly divided into two ...of Property (T) obtained either by restricting the class of considered representations or by replacing lack of ergodicity by a weaker ... See full document

... compact groups to topological ...relative Property (T) contains much more precise information than the bare information whether G has Property ...relative Property (T) for ... See full document

... out the following programme. First we define the notion of a partial translation structure (Definition 11) on a uniformly discrete metric space, which captures ge- ometrically the interplay between the left and the right ... See full document

... There is a more general notation of a modular multiplicative unitary, see [26], which is more natural in certain examples. However, at the cost of changing our space H, we can recover (A, ∆) from a different, but related, ... See full document

... It is not yet known which vista a practical quantum computer will follow. The authors of [3] developed a view of universal quantum computing based on 3-manifolds. In a nutshell, there exists a connection ... See full document

... In this section, we introduce the concepts of amenability and coamenability for an algebraic quantum group. We begin with the latter concept. Our definition is an adaptation of one we gave in [5] for a compact ... See full document

... and quantum modularity, there is yet another systematic way to connect mock-false pairs: the method of Rademacher ...modular groups, and later, it produced weight 1/2 mock modular forms [32, 49, ... See full document

... of quantum L´evy processes, developed by Sch¨ urmann and others, generalises the classical theory of L´evy processes on groups ([Hey]), and Skoro- hod’s theory of stochastic semigroups ([Sko]), to the ... See full document

... Since the time of Newton, di ff erential calculus demonstrates high e ffi ciency in describing physical phenomena. However, the infinitesimal analysis introduces infinities in the physical theories. This is often ... See full document

... compact quantum groups, [25], which, rather roughly, are C ∗ -bialgebras with invariant ...a quantum group as an abstract object G , and then write C 0 ( G ) for the C ∗ -algebra ... See full document

... abelian groups such that if G is a member of one of these families, then G has the R´ edei k-property for each k with 2k > ...abelian groups are the ... See full document

... the quantum isometry groups Q( , ) of ( , ) with presentation (4) is isomorphic to ⊕ ), where is a automorphism of compact quantum group Q(( , ) ) with ... See full document

... topological quantum field theory to maps from manifolds into topological ...Homotopy Quantum Field Theory(HQFT) which may be described as a version of a TQFT for closed oriented n-dimensional manifolds and ... See full document

... The whole setting of manifold invariants is extended to include manifolds with boundary, regarded as cobordisms between two subsets of their bound- ary components. The wider setting envisages a standard vector space for ... See full document

... Briefly, the organisation of the paper is as follows. We firstly introduce locally compact quantum groups, and then summarise the notion of a “morphism”. Compared to [24] we work with “left” multiplicative ... See full document

... basis property has all its elements of prime- power ...basis property is inherited by quotients and that a group with the basis property is ...soluble groups with all elements of prime-power ... See full document

... Quantum groups (which are algebras rather than groups) provide a generalization of familiar sym- metry concepts through extending the domain of classical group ...theory. Quantum groups ... See full document

... The whole setting of manifold invariants is extended to include manifolds with boundary, regarded as cobordisms between two subsets of their boundary com- ponents. The wider setting envisages a standard vector space for ... See full document

... closed quantum subgroup of a locally compact quantum ...of quantum groups while the latter can be related to an old definition of Podle´s from the theory of compact quantum ...classical ... See full document

... Of course it is natural to conjecture that the theorem of Casacuberta and Hilton remains true if one considers any fgp groups which are special or have, for an infinite number of primes,[r] ... See full document