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6 papers · 1 filter
A New Characterisation of Idempotent States on Finite and Compact Quantum Groups
Uwe Franz, Adam Skalski
We show that idempotent states on finite quantum groups correspond to pre-subgroups in the sense of Baaj, Blanchard, and Skandalis. It follows that the lattices formed by the idemp…
Convolution semigroups of states
J. Martin Lindsay, Adam Skalski
Convolution semigroups of states on a quantum group form the natural noncommutative analogue of convolution semigroups of probability measures on a locally compact group. Here we i…
A note on spectral triples and quasidiagonality
Adam Skalski, Joachim Zacharias
Spectral triples (of compact type) are constructed on arbitrary separable quasidiagonal C*-algebras. On the other hand an example of a spectral triple on a non-quasidiagonal algebr…
Quantum Isometry Groups of 0- Dimensional Manifolds
Jyotishman Bhowmick, Debashish Goswami, Adam Skalski
Quantum isometry groups of spectral triples associated with approximately finite-dimensional C*-algebras are shown to arise as inductive limits of quantum symmetry groups of corres…
Atomic Representations of Rank 2 Graph Algebras
Kenneth R. Davidson, Stephen C. Power, Dilian Yang
We provide a detailed analysis of atomic *-representations of rank 2 graphs on a single vertex. They are completely classified up to unitary equivalence, and decomposed into a dire…
Operator algebras associated with unitary commutation relations
Stephen C. Power, Baruch Solel
We define nonselfadjoint operator algebras with generators subject to the unitary commutation relations of the form \[ L_{e_i}L_{f_j} =…