- International Electronic Journal of Algebra
- Vol: 30 Issue: 30
- A CASIMIR ELEMENT INEXPRESSIBLE AS A LIE POLYNOMIAL
A CASIMIR ELEMENT INEXPRESSIBLE AS A LIE POLYNOMIAL
Authors : Rafael Reno S. Cantuba
Pages : 1-15
Doi:10.24330/ieja.969570
View : 11 | Download : 9
Publication Date : 2021-07-17
Article Type : Research
Abstract :Let $q$ be a scalar that is not a root of unity. We show that any nonzero polynomial in the Casimir element of the Fairlie-Odesskii algebra $U_q'(\mathfrak{so}_3)$ cannot be expressed in terms of only Lie algebra operations performed on the generators $I_1,I_2,I_3$ in the usual presentation of $U_q'(\mathfrak{so}_3)$. Hence, the vector space sum of the center of $U_q'(\mathfrak{so}_3)$ and the Lie subalgebra of $U_q'(\mathfrak{so}_3)$ generated by $I_1,I_2,I_3$ is direct.Keywords : Lie polynomial, Casimir element, quantum group, quantum algebra