### Abstract

In this letter we make three observations: (i) Given any Lie group, G, the (2+1)-Palatini action is equivalent to the Chern-Simons action for an "inhomogenized" Lie group, IG, constructed from G. (ii) Since the reduced phase space of the Chern-Simons theory based on any group G is the reduced configuration space of the Palatini theory based on the same G - i.e., the Chern-Simons theory for IG-one can introduce additional structure on the configuration and phase-spaces of Palatini theories -including (2+1)-gravity-which plays an important role in their quantization. (iii) Using the first observation, one can couple Chern-Simons matter to (2+1)-gravity in a straightforward way. We point out that there is, however, a qualitative difference between this coupling and that of matter with genuine, local degrees of freedom.

Original language | English (US) |
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Pages (from-to) | 56-60 |

Number of pages | 5 |

Journal | Physics Letters B |

Volume | 229 |

Issue number | 1-2 |

DOIs | |

State | Published - Oct 5 1989 |

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### All Science Journal Classification (ASJC) codes

- Nuclear and High Energy Physics

### Cite this

*Physics Letters B*,

*229*(1-2), 56-60. https://doi.org/10.1016/0370-2693(89)90155-X