Resumen de Polynomial identities and noncommutative versal torsors
Eli Aljadeff, Christian Kassel
To any cleft Hopf Galois object, i.e., any algebra obtained from a Hopf algebra H by twisting its multiplication with a two-cocycle a, we attach two �universal algebras� and . The algebra is obtained by twisting the multiplication of H with the most general two-cocycle s formally cohomologous to a. The cocycle s takes values in the field of rational functions on H. By construction, is a cleft H-Galois extension of a �big� commutative algebra . Any �form� of can be obtained from by a specialization of and vice versa. If the algebra is simple, then is an Azumaya algebra with center . The algebra is constructed using a general theory of polynomial identities that we set up for arbitrary comodule algebras; it is the universal comodule algebra in which all comodule algebra identities of are satisfied. We construct an embedding of into ; this embedding maps the center of into when the algebra is simple. In this case, under an additional assumption, , thus turning into a central localization of . We completely work out these constructions in the case of the four-dimensional Sweedler algebra
