Deformations of Quadratic Algebras with Antisymmetric Relations |
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| Authors: | Ji-Wei He |
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| Affiliation: | Department of Mathematics , Shaoxing College of Arts and Sciences , Shaoxing Zhejiang, Chinaand Department of Mathematics and Computer Science, University of Antwerp, Antwerp, Belgium |
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| Abstract: | 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. |
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| Keywords: | Calabi–Yau algebra PBW-deformation Weakly symmetric algebra |
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