Generalized twists and PBW-type deformations.

摘要

The main aim of this thesis is the introduction and study of a common generalization of J. Zhang's twisting systems and the notion of an algebra of I-type introduced by Tate and Van den Bergh. Following Zhang we call these generalized twists.;A homological characterization of a generalized twist is given. It is shown that the properties of being a Koszul algebra and, under a mild condition, of being a Koszul Artin-Schelter regular algebra are preserved under generalized twists.;The second part of this thesis shows how one can use the Poincare-Birkhoff-Witt type deformations of Braverman and Gaitsgory to construct algebras with nice homological properties. As an example, the Poincare-Birkhoff-Witt type deformations of the three dimensional Sklyanin algebra are calculated.