Research output: Contribution to journal › Article

Journal | Communications in Mathematical Physics |
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Date | Published - Sep 2010 |

Issue number | 3 |

Volume | 298 |

Number of pages | 27 |

Pages (from-to) | 585-611 |

Original language | English |

Given a symmetric decomposition of a semisimple Lie algebra , we define the notion of a -contractible quantized universal enveloping algebra (QUEA): for these QUEAs the contraction making abelian is nonsingular and yields a QUEA of . For a certain class of symmetric decompositions, we prove, by refining cohomological arguments due to Drinfel’d, that every QUEA of so obtained is isomorphic to a cochain twist of the undeformed envelope . To do so we introduce the -contractible Chevalley-Eilenberg complex and prove, for this class of symmetric decompositions, a version of Whitehead’s lemma for this complex. By virtue of the existence of the cochain twist, there exist triangular quasi-Hopf algebras based on these contracted QUEAs and, in the approach due to Beggs and Majid, the dual quantized coordinate algebras admit quasi-associative differential calculi of classical dimensions. As examples, we consider ¿-Poincaré in 3 and 4 spacetime dimensions.

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