Using principles of quantum symmetries we derive the algebraic part of the real spectral triple data for the standard Podleś quantum sphere: equivariant representation, chiral grading γ, reality structure J and the Dirac operator D, which has bounded commutators with the elements of the algebra and satisfies the first order condition.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-4,
author = {Ludwik D\k abrowski and Andrzej Sitarz},
title = {Dirac operator on the standard Podle\'s quantum sphere},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {49-58},
zbl = {1061.58004},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-4}
}
Ludwik Dąbrowski; Andrzej Sitarz. Dirac operator on the standard Podleś quantum sphere. Banach Center Publications, Tome 60 (2003) pp. 49-58. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-4/