61 citations · 438 across the 47 of their papers we have counts for
10 papers · 1 filter
A secondary index for non-Fredholm operators associated with quantum walks
Toshikazu Natsume, Ryszard Nest
We study an analogue of chirality operators associated with quantum walks on the binary tree. For those operators we introduce a K-theoretic invariant, an analogue of the index of…
Finiteness of metrics on state spaces
David Kyed, Ryszard Nest
We show that Connes' metric on the state space associated with a spectral triple is nowhere infinite exactly when it is globally bounded. Moreover, we produce a family of simple ex…
Projective representation theory for compact quantum groups and the quantum Baum-Connes assembly map
Kenny De Commer, Rubén Martos, Ryszard Nest
We study the theory of projective representations for a compact quantum group , i.e. actions of on for some Hilbert space . We show tha…
C*-Algebras over Topological Spaces: Filtrated K-Theory
Ralf Meyer, Ryszard Nest
We define the filtrated K-theory of a C*-algebra over a finite topological space X and explain how to construct a spectral sequence that computes the bivariant Kasparov theory over…
Twisted cyclic theory, equivariant KK theory and KMS States
Alan L. Carey, Sergey Neshveyev, Ryszard Nest +1
Recently, examples of an index theory for KMS states of circle actions were discovered, \cite{CPR2,CRT}. We show that these examples are not isolated. Rather there is a general fra…
Classification of Connections on Higher-Dimensional Non-Commutative Tori
Ryszard Nest, Rolf Dyre Svegstrup
If X is a full, finitely generated, projective module over a non-commutative torus, the Yang-Mills functional attains its minimum exactly on the flat connections on X. We classify…