Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres

Elmar Wagner. "Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres." Banach Center Publications 93.1 (2011): 225-240. <http://eudml.org/doc/282224>.

@article{ElmarWagner2011,
abstract = {It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is shown that the failure of the real structure to satisfy the commutant property is related to the failure of the universal R-matrix operator to be unitary.},
author = {Elmar Wagner},
journal = {Banach Center Publications},
keywords = {Podleś quantum sphere; quantum group; equivariant spectral triple; Dirac operator; Tomita operator; grading operator; Hopf *-algebra},
language = {eng},
number = {1},
pages = {225-240},
title = {Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres},
url = {http://eudml.org/doc/282224},
volume = {93},
year = {2011},
}

TY - JOUR
AU - Elmar Wagner
TI - Restricting the bi-equivariant spectral triple on quantum SU(2) to the Podleś spheres
JO - Banach Center Publications
PY - 2011
VL - 93
IS - 1
SP - 225
EP - 240
AB - It is shown that the isospectral bi-equivariant spectral triple on quantum SU(2) and the isospectral equivariant spectral triples on the Podleś spheres are related by restriction. In this approach, the equatorial Podleś sphere is distinguished because only in this case the restricted spectral triple admits an equivariant grading operator together with a real structure (up to infinitesimals of arbitrary high order). The real structure is expressed by the Tomita operator on quantum SU(2) and it is shown that the failure of the real structure to satisfy the commutant property is related to the failure of the universal R-matrix operator to be unitary.
LA - eng
KW - Podleś quantum sphere; quantum group; equivariant spectral triple; Dirac operator; Tomita operator; grading operator; Hopf *-algebra
UR - http://eudml.org/doc/282224
ER -