Journal of Lie Theory

no. 2
A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2)
Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 557-585
An analogue of a spectral triple over SUq(2) is constructed for which the usual assumption of bounded commutators with the Dirac operator fails. An analytic expression analogous to that for the Hochschild class of the Chern character for spectral triples yields a non-trivial twisted Hochschild 3-cocycle. The problems arising from the unbounded commutators are overcome by defining a residue functional using projections to cut down the Hilbert space.
DOI: 10.5802/jolt.682
Classification: 19K33, 19K56, 20G42, 46L80, 46L87,, 58B32, 58B34, 58J42, 58J20, 81R50
Keywords: Spectral triples, Dirac operators, cyclic cohomology, quantum groups, quantum SU(2), residue formulas, Calabi-Yau algebras 
@article{JOLT_2012_22_2_a11,
     author = {U. Kr\"ahmer and A. Rennie and R. Senior},
     title = {A {Residue} {Formula} for the {Fundamental} {Hochschild} {3-Cocycle} for {SU\protect\textsubscript{q}(2)}},
     journal = {Journal of Lie Theory},
     pages = {557--585},
     year = {2012},
     volume = {22},
     number = {2},
     doi = {10.5802/jolt.682},
     zbl = {1247.58007},
     url = {https://jolt.centre-mersenne.org/articles/10.5802/jolt.682/}
}
TY  - JOUR
AU  - U. Krähmer
AU  - A. Rennie
AU  - R. Senior
TI  - A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2)
JO  - Journal of Lie Theory
PY  - 2012
SP  - 557
EP  - 585
VL  - 22
IS  - 2
UR  - https://jolt.centre-mersenne.org/articles/10.5802/jolt.682/
DO  - 10.5802/jolt.682
ID  - JOLT_2012_22_2_a11
ER  - 
%0 Journal Article
%A U. Krähmer
%A A. Rennie
%A R. Senior
%T A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2)
%J Journal of Lie Theory
%D 2012
%P 557-585
%V 22
%N 2
%U https://jolt.centre-mersenne.org/articles/10.5802/jolt.682/
%R 10.5802/jolt.682
%F JOLT_2012_22_2_a11
U. Krähmer; A. Rennie; R. Senior. A Residue Formula for the Fundamental Hochschild 3-Cocycle for SUq(2). Journal of Lie Theory, Volume 22 (2012) no. 2, pp. 557-585. doi: 10.5802/jolt.682

Cited by Sources: