On trivialization of discriminant algebras of hyperbolic quadratic modules

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Abstract

For discriminant algebras of hyperbolic quadratic modules, defined according to Loos (Beiträge Algebra Geom 38(1):33–72, 1997), their trivializations and relation to Clifford algebras are described globally without using localization. In the process, specific descriptions of Pfaffian cocycles are given in the case of finitely generated projective modules.