Symmetry, Integrability and Geometry: Methods and Applications (SIGMA)

SIGMA 10 (2014), 086, 36 pages      arXiv:1403.0808
Contribution to the Special Issue on Deformations of Space-Time and its Symmetries

Matrix Bases for Star Products: a Review

Fedele Lizzi a, b, c and Patrizia Vitale a, b
a) Dipartimento di Fisica, Università di Napoli Federico II, Napoli, Italy
b) INFN, Sezione di Napoli, Italy
c) Institut de Ciéncies del Cosmos, Universitat de Barcelona, Catalonia, Spain

Received March 04, 2014, in final form August 11, 2014; Published online August 15, 2014

We review the matrix bases for a family of noncommutative $\star$ products based on a Weyl map. These products include the Moyal product, as well as the Wick-Voros products and other translation invariant ones. We also review the derivation of Lie algebra type star products, with adapted matrix bases. We discuss the uses of these matrix bases for field theory, fuzzy spaces and emergent gravity.

Key words: noncommutative geometry; star products; matrix models.

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