TY - JOUR
T1 - Finite-dimensional irreducible modules of the Bannai–Ito algebra at characteristic zero
AU - Huang, Hau Wen
N1 - Publisher Copyright:
© 2020, Springer Nature B.V.
PY - 2020/9/1
Y1 - 2020/9/1
N2 - Assume that F is algebraically closed with characteristic 0. A central extension BI of the Bannai–Ito algebras is a unital associative F-algebra generated by X, Y, Z, and the relations assert that each of {X,Y}-Z,{Y,Z}-X,{Z,X}-Yis central in BI. In this paper, we classify the finite-dimensional irreducible BI-modules up to isomorphism. As we will see, the elements X, Y, Z are not always diagonalizable on finite-dimensional irreducible BI-modules.
AB - Assume that F is algebraically closed with characteristic 0. A central extension BI of the Bannai–Ito algebras is a unital associative F-algebra generated by X, Y, Z, and the relations assert that each of {X,Y}-Z,{Y,Z}-X,{Z,X}-Yis central in BI. In this paper, we classify the finite-dimensional irreducible BI-modules up to isomorphism. As we will see, the elements X, Y, Z are not always diagonalizable on finite-dimensional irreducible BI-modules.
KW - Bannai–Ito algebra
KW - Irreducible modules
KW - Universal property
UR - http://www.scopus.com/inward/record.url?scp=85087514986&partnerID=8YFLogxK
U2 - 10.1007/s11005-020-01306-9
DO - 10.1007/s11005-020-01306-9
M3 - 期刊論文
AN - SCOPUS:85087514986
SN - 0377-9017
VL - 110
SP - 2519
EP - 2541
JO - Letters in Mathematical Physics
JF - Letters in Mathematical Physics
IS - 9
ER -