Wyniki wyszukiwania

1

Equivariant spectral triples

100%

Sitarz A.

Banach Center Publications

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2003

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tom 61

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nr 1

231-263

EN

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.

2

Dirac operator on the standard Podleś quantum sphere

63%

Dąbrowski L., Sitarz A.

Banach Center Publications

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2003

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tom 61

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nr 1

49-58

EN

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.

3

κ-deformation, affine group and spectral triples

51%

Iochum B., Masson T., Sitarz A.

Banach Center Publications

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2012

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tom 98

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nr 1

261-291

EN

A regular spectral triple is proposed for a two-dimensional κ-deformation. It is based on the naturally associated affine group G, a smooth subalgebra of C*(G), and an operator 𝓓 defined by two derivations on this subalgebra. While 𝓓 has metric dimension two, the spectral dimension of the triple is one. This bypasses an obstruction described in [35] on existence of finitely-summable spectral triples for a compactified κ-deformation.

Ograniczanie wyników

3 Banach Center Publications

3 Sitarz A.

1 Dąbrowski L.

1 Iochum B.

1 Masson T.

1 2012

2 2003

Equivariant spectral triples

Dirac operator on the standard Podleś quantum sphere

κ-deformation, affine group and spectral triples