On the Structure of Quantum Toroidal Superalgebra ℰm|n

Recently the quantum toroidal superalgebra ℰ m | n associated with g l m | n was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac–Moody algebra. The quantum toroidal superalgebra ℰ m | n exploits infinite sequences of generators and relations of the form, which are called Drinfeld...

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Bibliographic Details
Published inActa mathematica Sinica. English series Vol. 39; no. 11; pp. 2117 - 2138
Main Authors Wu, Xiang Hua, Lin, Hong Da, Zhang, Hong Lian
Format Journal Article
LanguageEnglish
Published Berlin/Heidelberg Springer Berlin Heidelberg 2023
Springer Nature B.V
Subjects
Algebra
Infinite elements
Mathematical analysis
Mathematics
Mathematics and Statistics
17B67
Drinfeld realization
17B37
Quantum toroidal superalgebra
Lie superalgebra
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Summary:Recently the quantum toroidal superalgebra ℰ m | n associated with g l m | n was introduced by L. Bezerra and E. Mukhin, which is not a quantum Kac–Moody algebra. The quantum toroidal superalgebra ℰ m | n exploits infinite sequences of generators and relations of the form, which are called Drinfeld realization. In this paper, we use only finite set of generators and relations to define an associative algebra ℰ m | n ′ and show that there exists an epimorphism from ℰ m | n ′ to the quantum toroidal superalgebra ℰ m | n . In particular, the structure of ℰ m | n ′ enjoys some properties like Drinfeld–Jimbo realization.
ISSN:1439-8516
1439-7617
DOI:10.1007/s10114-023-2426-x