Deformation Quasi-Hopf Algebras of Non-semisimple Type from Cochain Twists

Young, Charles A. S. and Zegers, Robin (2010) Deformation Quasi-Hopf Algebras of Non-semisimple Type from Cochain Twists. Communications in Mathematical Physics, 298 (3). pp. 585-611. ISSN 0010-3616
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One way to obtain Quantized Universal Enveloping Algebras (QUEAs) of non-semisimple Lie algebras is by contracting QUEAs of semisimple Lie algebras. We prove that every contracted QUEA in a certain class is a cochain twist of the corresponding undeformed universal envelope. Consequently, these contracted QUEAs possess a triangular quasi-Hopf algebra structure. As examples, we consider kappa-Poincare in 3 and 4 spacetime dimensions


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