Preprint arXiv:0911.5287, submitted
Mathematics Subject Classification (2000): 20D25, 20J06, 16S34, 16W30
Abstract. We present a way of twisting G-algebras, which in particular produces braided-commutative algebras from commutative ones. The procedure is a strict analogue of a classical construction in algebraic geometry based on torsors. As a result, we have a very natural way of constructing familiar non-commutative spaces such as the quantum tori. In order to twist an algebra we need to endow it with an action of a finite group G and we must choose a "non-commutative bitorsor", which amounts to an element in the second lazy cohomology group of the Hopf algebra of functions on G. We illustrate our twisting procedure with several examples together with explicit calculations.
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(30 novembre 2009)