... q-deformation of U(sl(2)). After this we describe the general case U, (g). Example 2.1 Let k = C and q e C", not a root of unity. Let U,(sl(2)) be the non-commutative - H + H. algebra generated by 1 ... =# - 1 (the notation is meant to ...
... Q, = "Tl A # (a)da 0 For Q = const , the integrals in the numerators are readily calculated: l in knl } Q?n (x) dx =# [1 – cos knl +# (1 – ch K.)] - For the computation of the integrals in the denominator, we may again use Table l. In ...
... q"(1- 2bx°), [Q =# (1 - bx*] o This is the pressure treated in the previous section; see (4.1). Problem II: (5.2) q = q x", [Q = + x'] . sk In (5.1) and (5.2), the constant q is the amplitude of the pressure. We define a new variable y ...
... q| < 1, then # k2 (-aid").(a d'). (i) % (q) TE f(q, q) = 1 + 2 Q 2: 2 2 2 3. k=l (q; q"). (-q"; q"). OC) (g";a") (ii) ... =# n=l n=l 1 + q 2n l 2) 5 CO n' (1 - "in a ") (dia”). Go",a which is a famous identity of Euler. Substituting (22.2) ...
... 1-simulate it Theorem 1. For k > 1, T € {o, di, de, f}, for any A, the following containments hold: 1. – C =#1 ... [q] denote the equivalence class of q e Q with respect to ~. The quotient of A with respect to ~ is the automaton A/~ = (X ...
... 1 kak :5C, nEN. k=1 Thus the desired result follows from Theorem 3.3.1 (ii). Another direct consequence of Theorem 3.3.1 is the construction of some special function's suggesting that Qp is a large subspace of Dp. Example 3.3.1. Let p E n( ...