A CASIMIR ELEMENT INEXPRESSIBLE AS A LIE POLYNOMIAL

Authors : Rafael Reno S CANTUBA

Pages : 1-15

Doi:10.24330/ieja.969570

View : 13 | Download : 10

Publication Date : 2021-07-17

Article Type : Research Paper

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 $U_q`insert ignore into journalissuearticles values(\mathfrak{so}_3);$ 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 $U_q`insert ignore into journalissuearticles values(\mathfrak{so}_3);$. Hence, the vector space sum of the center of $U_q`insert ignore into journalissuearticles values(\mathfrak{so}_3);$ and the Lie subalgebra of $U_q`insert ignore into journalissuearticles values(\mathfrak{so}_3);$ generated by $I_1,I_2,I_3$ is direct.
Keywords : Lie polynomial, Casimir element, quantum group, quantum algebra