Symmetries in connected graded algebras and their PBW-deformations

Yongjun Xu; Xin Zhang

Czechoslovak Mathematical Journal (2023)

  • Volume: 73, Issue: 4, page 1255-1272
  • ISSN: 0011-4642

Abstract

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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 𝒦 2 algebra 𝒜 which was introduced to compute the cohomology ring of the Fomin-Kirillov algebra ℱ𝒦 3 , and explicitly construct all the (self-)symmetric and sign-(self-)symmetric PBW-deformations of 𝒜 .

How to cite

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Xu, Yongjun, and Zhang, Xin. "Symmetries in connected graded algebras and their PBW-deformations." Czechoslovak Mathematical Journal 73.4 (2023): 1255-1272. <http://eudml.org/doc/299505>.

@article{Xu2023,
abstract = {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 $\mathcal \{A\}$.},
author = {Xu, Yongjun, Zhang, Xin},
journal = {Czechoslovak Mathematical Journal},
keywords = {connected graded algebra; PBW-deformation; self-symmetry; sign-symmetry; $\mathcal \{K\}_2$ algebra},
language = {eng},
number = {4},
pages = {1255-1272},
publisher = {Institute of Mathematics, Academy of Sciences of the Czech Republic},
title = {Symmetries in connected graded algebras and their PBW-deformations},
url = {http://eudml.org/doc/299505},
volume = {73},
year = {2023},
}

TY - JOUR
AU - Xu, Yongjun
AU - Zhang, Xin
TI - Symmetries in connected graded algebras and their PBW-deformations
JO - Czechoslovak Mathematical Journal
PY - 2023
PB - Institute of Mathematics, Academy of Sciences of the Czech Republic
VL - 73
IS - 4
SP - 1255
EP - 1272
AB - 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 $\mathcal {A}$.
LA - eng
KW - connected graded algebra; PBW-deformation; self-symmetry; sign-symmetry; $\mathcal {K}_2$ algebra
UR - http://eudml.org/doc/299505
ER -

References

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