Back to Search
Start Over
The [formula omitted]-symmetric down-up algebra.
- Source :
-
Journal of Algebra . Oct2024, Vol. 655, p862-896. 35p. - Publication Year :
- 2024
-
Abstract
- In 1998, Georgia Benkart and Tom Roby introduced the down-up algebra A. The algebra A is associative, noncommutative, and infinite-dimensional. It is defined by two generators A , B and two relations called the down-up relations. In the present paper, we introduce the Z 3 -symmetric down-up algebra A. We define A by generators and relations. There are three generators A , B , C and any two of these satisfy the down-up relations. We describe how A is related to some familiar algebras in the literature, such as the Weyl algebra, the Lie algebras sl 2 and sl 3 , the sl 3 loop algebra, the Kac-Moody Lie algebra A 2 (1) , the q -Weyl algebra, the quantized enveloping algebra U q (sl 2) , and the quantized enveloping algebra U q (A 2 (1)). We give some open problems and conjectures. [ABSTRACT FROM AUTHOR]
- Subjects :
- *QUANTUM groups
*KAC-Moody algebras
*ALGEBRA
*LIE algebras
*NONCOMMUTATIVE algebras
Subjects
Details
- Language :
- English
- ISSN :
- 00218693
- Volume :
- 655
- Database :
- Academic Search Index
- Journal :
- Journal of Algebra
- Publication Type :
- Academic Journal
- Accession number :
- 177880755
- Full Text :
- https://doi.org/10.1016/j.jalgebra.2023.09.039