The purpose of this report is to generalize the R-matrix theory of the quan- tum groups [1] to the case of all quantum matrix unitary Cayley-Klein groups.
J. Phys. A: Math. Gen., 1993, v. 26, L5–L8.
The matrix quantum unitary Cayley-Klein groups. N.A.Gromov Komi Scientific Centre, Russian Academy of Sciences, Syktyvkar 167000, Russia
The purpose of this report is to generalize the R-matrix theory of the quantum groups [1] to the case of all quantum matrix unitary Cayley-Klein groups which also include the quantum groups of the degenerate hermitic forms. Let Rq matrix is as in the case of An (or su(n + 1)) [1] , i.e. Rq = q
n X
n X
ekk ⊗ ekk +
ekk ⊗ emm + (q − q −1 )
(ekm )ij = δik δjm ,
ekm ⊗ emk ,
k,m=0 k>m
k,m=0 k6=m
k=0
n X
k, m, i, j, = 0, 1, . . . , n.
(1)
Let us define the algebra Aq (j) as the associative C-algebra generated by the noncommutative elements k ≥ m;
(T (j))km = tkm , Jkm = 1, k ≥ m,
Jkm =
m Y
jr , k < m,
2 (T (j))km = tkm Jkm ,
k
