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Symmetries in connected graded algebras and their PBW-deformations
Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1255-1272 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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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 $\mathcal {K}_2$ 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 $\mathcal {A}$.
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 $\mathcal {A}$.
DOI : 10.21136/CMJ.2023.0511-22
Classification : 16S80
Keywords: connected graded algebra; PBW-deformation; self-symmetry; sign-symmetry; $\mathcal {K}_2$ algebra 
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     title = {Symmetries in connected graded algebras and their {PBW-deformations}},
     journal = {Czechoslovak Mathematical Journal},
     pages = {1255--1272},
     year = {2023},
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Xu, Yongjun; Zhang, Xin. Symmetries in connected graded algebras and their PBW-deformations. Czechoslovak Mathematical Journal, Tome 73 (2023) no. 4, pp. 1255-1272. doi: 10.21136/CMJ.2023.0511-22

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