### Abstract

We give a simplified formula for the star product on CP^n_L, which enables us to define a twist element suited for discussing a Drinfeld twist like structure on fuzzy complex projective spaces. The existence of such a twist will have several consequences for field theories on fuzzy spaces, some of which we discuss in the present paper. As expected, we find that the twist of the coproduct is trivial for the generators of isometries on CP^n_L. Furthermore, the twist allows us to define a covariant tensor calculus on CP^n_L from the perspective of the standard embedding of CP^n in flat Euclidean space. That is, we find a representation of a truncated subgroup of the diffeomorphisms on CP^n on the algebra of functions on CP^n_L. Using this calculus, we eventually write down an Einstein-Hilbert action on the fuzzy sphere, which is invariant under twisted diffeomorphisms.

Original language | English |
---|---|

Pages (from-to) | 291-312 |

Number of pages | 22 |

Journal | Classical and Quantum Gravity |

Volume | 24 |

Issue number | 2 |

DOIs | |

Publication status | Published - 21 Jan 2007 |

## Fingerprint Dive into the research topics of 'Drinfeld twist and general relativity with fuzzy spaces'. Together they form a unique fingerprint.

## Cite this

Kürkçüoglu, S., & Saemann, C. (2007). Drinfeld twist and general relativity with fuzzy spaces.

*Classical and Quantum Gravity*,*24*(2), 291-312. https://doi.org/10.1088/0264-9381/24/2/003