Maximally extended sl(2|2), q-deformed d(2,1;epsilon) and 3D kappa-Poincar\'e

We show that the maximal extension sl(2) times psl(2|2) times C3 of the sl(2|2) superalgebra can be obtained as a contraction limit of the semi-simple superalgebra d(2,1;epsilon) times sl(2). We reproduce earlier results on the corresponding q-deformed Hopf algebra and its universal R-matrix by means of contraction. We make the curious observation that the above algebra is related to kappa-Poincar\'e symmetry. When dropping the graded part psl(2|2) we find a novel one-parameter deformation of the 3D kappa-Poincar\'e algebra. Our construction also provides a concise exact expression for its universal R-matrix.Comment: 25 page

The Prevalence of Polyneuropathy in Type 2 Diabetes Subgroups Based on HOMA2 Indices of β-Cell Function and Insulin Sensitivity

OBJECTIVE Metabolic syndrome components may cumulatively increase the risk of diabetic polyneuropathy (DPN) in type 2 diabetes mellitus (T2DM) patients, driven by insulin resistance and hyperinsulinemia. We investigated the prevalence of DPN in three T2DM subgroups based on indices of b-cell function and insulin sensitivity. RESEARCH DESIGN AND METHODS We estimated b-cell function (HOMA2-B) and insulin sensitivity (HOMA2-S) in 4,388 Danish patients with newly diagnosed T2DM. Patients were categorized into subgroups of hyperinsulinemic (high HOMA2-B, low HOMA2-S), classical (low HOMA2-B, low HOMA2-S), and insulinopenic (low HOMA2-B, high HOMA2-S) T2DM. After a median follow-up of 3 years, patients filled the Michigan Neuropathy Screening Instrument questionnaire (MNSIq) to identify DPN (score ‡ 4). We used Poisson regression to calculate adjusted prevalence ratios (PRs) for DPN, and spline models to examine the association with HOMA2-B and HOMA2-S. RESULTS A total of 3,397 (77%) patients filled in the MNSIq. The prevalence of DPN was 23% among hyperinsulinemic, 16% among classical, and 14% among insulinopenic pa-tients. After adjusting for demographics, diabetes duration and therapy, lifestyle behaviors, and metabolic syndrome components (waist circumference, triglycer-ides, HDL cholesterol, hypertension, and HbA1c), the PR of DPN was 1.35 (95% CI 1.15–1.57) for the hyperinsulinemic compared with the classical patients. In spline analyses, we observed a linear relation of higher DPN prevalence with increasing HOMA2-B, independent of both metabolic syndrome components and HOMA2-S. CONCLUSIONS Hyperinsulinemia marked by high HOMA2-B is likely an important risk factor for DPN beyond metabolic syndrome components and insulin resistance. This should be considered when developing interventions to prevent DPN