We present the review of noncommutative symmetries applied to Connes' formulation of spectral triples. We introduce the notion of equivariant spectral triples with Hopf algebras as isometries of noncommutative manifolds, relate it to other elements of theory (equivariant K-theory, homology, equivariant differential algebras) and provide several examples of spectral triples with their isometries: isospectral (twisted) deformations (including noncommutative torus) and finite spectral triples.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-16,
author = {Andrzej Sitarz},
title = {Equivariant spectral triples},
journal = {Banach Center Publications},
volume = {60},
year = {2003},
pages = {231-263},
zbl = {1061.58007},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-16}
}
Andrzej Sitarz. Equivariant spectral triples. Banach Center Publications, Tome 60 (2003) pp. 231-263. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-bc61-0-16/