Finite-Dimensional Irreducible Modules of the Racah Algebra at Characteristic Zero
Assume that 𝔽 is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative 𝔽-algebra defined by generators and relations in the following way. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D and that each of [A, D]+AC−B...
Saved in:
| Published in: | Symmetry, Integrability and Geometry: Methods and Applications |
|---|---|
| Date: | 2020 |
| Main Authors: | , |
| Format: | Article |
| Language: | English |
| Published: |
Інститут математики НАН України
2020
|
| Online Access: | https://nasplib.isofts.kiev.ua/handle/123456789/210592 |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| Journal Title: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Cite this: | Finite-Dimensional Irreducible Modules of the Racah Algebra at Characteristic Zero. Hau-Wen Huang and Sarah Bockting-Conrad. SIGMA 16 (2020), 018, 17 pages |
Institution
Digital Library of Periodicals of National Academy of Sciences of Ukraine| Summary: | Assume that 𝔽 is an algebraically closed field with characteristic zero. The Racah algebra ℜ is the unital associative 𝔽-algebra defined by generators and relations in the following way. The generators are A, B, C, D, and the relations assert that [A, B]=[B, C]=[C, A]=2D and that each of [A, D]+AC−BA, [B, D]+BA−CB, [C, D]+CB−AC is central in ℜ. In this paper, we discuss the finite-dimensional irreducible ℜ-modules in detail and classify them up to isomorphism. To do this, we apply an infinite-dimensional ℜ-module and its universal property. We additionally give the necessary and sufficient conditions for A, B, C to be diagonalizable on finite-dimensional irreducible ℜ-modules.
|
|---|---|
| ISSN: | 1815-0659 |