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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 algebra which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra , and explicitly construct all the (self-)symmetric and sign-(self-)symmetric...
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