Rtt Is The Sense Of A Quantum Algebra

The theories centering about Yang-Baxter equation (YBE) are systematic and successful theories when they are used to deal with some nonlinear model. RTT relation generaliazes a lot of commrtation and it is a theoretic frame which limits complete integrable system.Giving (?)(u) as YBE's solrtion, theories about quantum groups which include Yan-gian and quantum algebras can be derived from RTT relation. There when YBE's solution is a retional solution,Yangian can be obtained from RTT relation,while quatntum algebras can be given by RTT relation when YBE' solutionis a trigonometric solution.Under infinite condition because trigonometric solution will degenerateinto retional solution quantum algebras will change into Yangian.The process of this paper is that T(x) is extended by x and thar we impose interrupted condition on T(x),that is to say that T(x) has the maximum power of x. We can obtain commutation relations between the elemements Tab,(a, b = 1,2) of two matrix from RTT relation.In this paper ,T(x) reads x2T(2) + T(0) + x-2T2T(-2).The form of T(2) and T(-2) read the same as L(1) and L(-1) in the formmula L(x) = xL(1) + x-1L(-1) by experience.Goiny step further by experience and theoretic calculation. We guass the forms of elements of T(0) and obtion the new algebras which are different from simple quantum algebras.Here we name then Yq(sl(2)) algebras.Yq(sl(2)) algebras' correctitude may be exammined by the XXZ model of two lattices. Just as the consequence of the inference, this new algebras will change into Yangian undeer infinite condition .We obtion conclusion: Yangian is Lie algebras' extension and Lie algebras are the subalgebras of Yangian; Yq(sl(2))algebras are simple quantum algebras' extension and simple quantum algebras are Yq(sl(2)) algebras' subalgebras simple quantum algebras will change into Lie algebras under infinite condition,that is to say that simple quantum algebras are q- deformed Lie algebras; Yq(sl(2)) algebras will change into Yangian under infinite condition,that is to say Yq(sl(2)) algebras are q?deformed Yangian.Yq(sl(2)) algebras describe the new symmetry, as is Yangian, whichnonlinear complete quantum integrable model have,and Yq(sl(2)) algebras can also construct shift operator between the two different quantum states.