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Deformations of Quadratic Algebras with Antisymmetric Relations

A finitely generated quadratic algebra with antisymmetric generating relations is called a weakly symmetric algebra. The automorphism group and Calabi–Yau property of a Poincaré–Birkhoff–Witt (PBW)-deformation of a weakly symmetric algebra are discussed. It is shown that the Calabi–Yau property of a PBW-deformation of a weakly symmetric algebra is equivalent to that of the corresponding augmented PBW-deformation under some mild conditions.