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In this paper, we study the Green ring (or the representation ring) of Drinfeld quantum double D( H) of Sweedler's four-dimensional Hopf algebra H. We first give the decompositions of the tensor products of finite dimensional indecomposable modules into the direct sum of indecomposable modules over D( H). Then we describe the structure of the Green ring r( D( H)) of D( H) and show that r( D( H)) is generated, as a ring, by infinitely many elements subject to a family of relations. [ABSTRACT FROM AUTHOR]

Quiver Hopf algebras are classified by means of ramification systems with irreducible representations. This leads to the classification of Nichols algebras over group algebras and pointed Hopf algebras of type one. [ABSTRACT FROM AUTHOR]

In the previous papers[1,2] we constructed an n4-dimensional Hopf algebra H,(p,q) which is isomorphic to Drinfeld quantum double D(A,(co)) of Taft's Hopf algebra A,(co) if p 5@ 0 and co = q-1 is a primitive nth root of unity, and studied the irreducible representations of H,(1, q). In this paper, we continue our study and examine the irreducible representations of H,(1,q) when q is any nth root of 1. We give the structures of all simple H,(1, q)-modules, and then classify them. We show that there are only n2 distinct simple H, (1, q)modules up to isomorphism. Though H,(1,q) is not a bialgebra, we show that the tensor product of two simple H, (1, q)-modules possesses an H, (1, q)-module structure in a way similar to the case that q is a primitive nth root of 1. Then we give a sufficient and necessary condition for the tensor product of two simple H[sub n](1, q)-modules to be semisimple. More generally, we describe the structure of socal of the tensor product. [ABSTRACT FROM AUTHOR]

Objective: To evaluate whether combined oral oxycodone hydrochloride controlled-release tablets plus paracetamol and tramadol hydrochloride tablets is better than epidural analgesia with respect to uterine cramping pain control and side effects after cesarean section., Methods: Sixty consecutive patients scheduled for cesarean section from April to May, 2010 were randomized to either patient-controlled epidural analgesia with 0.1% ropivacaine, 0.1 µg/ml sufentanil (for postoperative 48 h) plus injected pethidine on demand (EDA group) or controlled-release oxycodone (2 × 15 mg for 1st postoperative 24 h; 2 × 10 mg for 2nd postoperative 24 h), paracetamol & tramadol hydrochloride tablets (8 × 1 tablet for postoperative 48 h) orally plus pethidine injection on demand (OXY group). Two groups were compared with respects to uterine cramping pain control when the oxytocin infusion (20 U plus 500 ml 5% glucose solution, iv. gtt within 2 h) once per day for postoperative 3 days as determined by the means of a visual analogue scale (VAS), pethidine consumption, side effects and costs., Results: The EDA group experienced significant more pain than the OXY group when the oxytocin infusion was administered (mm) [50.0 (15.0, 72.5) vs 25.0 (0, 40.0), 60.0 (47.5, 72.5) vs 20.0 (0, 30.0), 35.0 (20.0, 50.0) vs 0 (0, 20.0)]. all P < 0.05). Pethidine was used for pain control in 2 patients (150 mg total) of EDA group during the oxytocin infusion whereas none of the OXY group received an injection of pethidine. There was a higher level of maternal satisfaction with a lower analgesic dose in the EDA group (80.9 ± 9.3 vs 90.0 ± 9.8, P < 0.01). The median duration of hospital stay was around 5 days in both groups., Conclusion: Postoperative pain control after cesarean section with the above combined regimen is superior to EDA in terms of a lower cost and a higher level of maternal satisfaction.