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Keywords:
connected graded algebra; PBW-deformation; self-symmetry; sign-symmetry; $\mathcal {K}_2$ algebra
connected graded algebra; PBW-deformation; self-symmetry; sign-symmetry; $\mathcal {K}_2$ algebra
Summary:
We focus on connected graded algebras and their PBW-deformations endowed with additional symmetric structures. Many well-known algebras such as negative parts of Drinfeld-Jimbo's quantum groups, cubic Artin-Schelter algebras and three-dimensional Sklyanin algebras appear in our research framework. As an application, we investigate a $\mathcal {K}_2$ algebra $\mathcal {A}$ which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra $\mathcal {FK}_3$, and explicitly construct all the (self-)symmetric and sign-(self-)symmetric PBW-deformations of $\mathcal {A}$.
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