Y_q (s1 (2)) Algebra Of Further Study

The theories centering upon Yang-Baxter equation (YBE) promote the research on quantum complete integrable model and are systematic and successful theories when they are used to deal with some nonlinear model. Especially RTT relation constituted by L.D.Faddeev generalizes a lot of commutation and it is a theoretic frame which limits complete integrable system. Givingas YBE's solution, quantum groups including and quantum algebras can be derived from RTT relation. When YBE's solution is a rational solution, can be obtained from RTT relation, while quantum algebras can be given by RTT relation when YBE's solution is a trigonometric solution.The content of this paper is that is extended by and we impose interrupted condition on , that is to say, has the maximum power of . We can obtain the commutation among the elements of two matrix from RTT relation. In this paper, reads , namely in correspondence with the condition of three particles. and all read simple quantum algebras. We can confirm the commutation between the elements of and those of . Accordingly we are able to find the new algebras relations which are different from simple quantum algebras. This is a new kind of quantum algebras, which is temporarily called algebras. Then we attempt to discuss the long-range interaction among the lattices. We mainly make use of essential commutation pertaining to algebras and obtain the limiting equation, which the coefficients must comply to. It can be seen that we gained good results.