On the Quantum Stucture of the Universal Enveloping Algebra of the Lie Algebra St (2)

The structure of Hopf co-Poisson algebra on the universal enveloping algebra U(S7(2)) of Lie algebra S7(2) is determined with the help of a solution of the Yang-Baxter equation. Using this solution, a bracket on the dual space of Lie algebra ST(2) is also determined. This cobracket on ST(2) induces a deformation of the universal enveloping algebra U(S7(2)) which has a Hopf algebra structure, as we shall verify. This Hopf algebra is called the quantum group associated to a universal enveloping algebra.