Representations of the q-deformed algebra Uq(iso2)U_q({\rm iso}_2)

An algebra homomorphism $\psi$ from the q-deformed algebra $U_q({\rm iso}_2)$ with generating elements $I$, $T_1$, $T_2$ and defining relations $[I,T_2]_q=T_1$, $[T_1,I]_q=T_2$, $[T_2,T_1]_q=0$ (where $[A,B]_q=q^{1/2}AB-q^{-1/2}BA$) to the extension ${\hat U}_q({\rm m}_2)$ of the Hopf algebra $U_q({\rm m}_2)$ is constructed. The algebra $U_q({\rm iso}_2)$ at $q=1$ leads to the Lie algebra ${\rm iso}_2 \sim {\rm m}_2$ of the group ISO(2) of motions of the Euclidean plane. The Hopf algebra $U_q({\rm m}_2)$ is treated as a Hopf $q$-deformation of the universal enveloping algebra of ${\rm iso}_2$ and is well-known in the literature. Not all irreducible representations of $U_q({\rm m}_2)$ can be extended to representations of the extension ${\hat U}_q({\rm m}_2)$. Composing the homomorphism $\psi$ with irreducible representations of ${\hat U}_q({\rm m}_2)$ we obtain representations of $U_q({\rm iso}_2)$. Not all of these representations of $U_q({\rm iso}_2)$ are irreducible. The reducible representations of $U_q({\rm iso}_2)$ are decomposed into irreducible components. In this way we obtain all irreducible representations of $U_q({\rm iso}_2)$ when $q$ is not a root of unity. A part of these representations turns into irreducible representations of the Lie algebra iso$_2$ when $q\to 1$. Representations of the other part have no classical analogue.Comment: 12 pages, LaTe

Global shifts, theoretical shifts: changing geographies of religion

10.1177/0309132510362602Progress in Human Geography346755-77

High seroprevalence of Toxoplasma gondii infection in a subset of Mexican patients with work accidents and low socioeconomic status

<p>Abstract</p> <p>Background</p> <p><it>Toxoplasma gondii </it>has been associated with reflex impairment and traffic accidents. It is unknown whether <it>Toxoplasma </it>infection might be associated with work accidents. Therefore, using a case-control seroprevalence study design, 133 patients with a recent work accident and 266 control subjects of the general population from the same region were examined with enzyme-linked immunoassays for the presence and levels of anti-<it>Toxoplasma </it>IgG antibodies and anti-<it>Toxoplasma </it>IgM antibodies. Socio-demographic, work, clinical and behavioral characteristics from each worker were obtained.</p> <p>Results</p> <p>Eleven (8.3%) of 133 patients, and 14 (5.3%) of 266 controls had anti-<it>T. gondii </it>IgG antibodies. Anti-<it>T. gondii </it>IgG levels were higher than 150 IU/ml in 8 (6%) patients and 10 (3.8%) controls. Anti-<it>T. gondii </it>IgM antibodies were found in one (0.8%) of the workers, and in 6 (2.3%) of the controls. No statistically significant differences in the IgG seroprevalences, frequencies of high IgG levels, and IgM seroprevalences among patients and controls were found. In contrast, a low socio-economic level in patients with work accidents was associated with <it>Toxoplasma </it>seropositivity (<it>P </it>= 0.01). Patients with work accidents and low socioeconomic status showed a significantly (OR = 3.38; 95% CI: 0.84-16.06; <it>P </it>= 0.04) higher seroprevalence of <it>T. gondii </it>infection than controls of the same socioeconomic status (15.1% vs. 5%, respectively). Multivariate analysis showed a positive association of <it>T. gondii </it>infection with boar meat consumption (OR = 3.04; 95% CI: 1.03-8.94; <it>P </it>= 0.04). In contrast, a negative association between <it>T. gondii </it>infection and national trips (OR = 0.40; 95% CI: 0.17-0.96; <it>P </it>= 0.04), sausage consumption (OR = 0.20; 95% CI: 0.05-0.68; <it>P </it>= 0.01), and ham consumption (OR = 0.16; 95% CI: 0.05-0.51; <it>P </it>= 0.002) was found.</p> <p>Conclusions</p> <p>In the study described here seropositivity to <it>T. gondii </it>was associated to work accidents in a subset of patients with low socioeconomic status. This is the first report of an association of <it>T. gondii </it>infection and work accidents. Further studies to confirm our results are needed. Results may help in designing optimal prevention strategies to avoid <it>T. gondii </it>infection.</p

Toxoplasma gondii infection in workers occupationally exposed to unwashed raw fruits and vegetables: a case control seroprevalence study

<p>Abstract</p> <p>Background</p> <p>Through a case control seroprevalence study, we sought to determine the association of <it>Toxoplasma gondii </it>infection with occupational exposure to unwashed raw fruits and vegetables.</p> <p>Methods</p> <p>Subjects, numbering 200, who worked growing or selling fruits and vegetables, and 400 control subjects matched by age, gender, and residence were examined by enzyme immunoassays for the presence of anti-<it>Toxoplasma </it>IgG and IgM antibodies. Socio-demographic, clinical, and behavioral characteristics from the study subjects were obtained.</p> <p>Results</p> <p>Of the 200 fruit and vegetable workers, 15 (7.5%) of whom, and 31 (7.8%) of the 400 controls were positive for anti-<it>Toxoplasma </it>IgG antibodies (<it>P </it>= 0.96). Anti-<it>Toxoplasma </it>IgM antibodies were found in 2 (1%) of the fruit workers and in 11 (2.8%) of the control subjects (<it>P </it>= 0.23). Seroprevalence of <it>Toxoplasma </it>antibodies increased with age (<it>P </it>= 0.0004). In addition, seropositivity to <it>Toxoplasma </it>was associated with ill status (<it>P </it>= 0.04), chronic tonsillitis (<it>P </it>= 0.03), and reflex impairment (<it>P </it>= 0.03). Multivariate analysis showed that <it>Toxoplasma </it>infection was associated with consumption of raw meat (OR = 5.77; 95% CI: 1.15-28.79; <it>P </it>= 0.03), unwashed raw fruits (OR = 2.50; 95% CI: 1.11-5.63; <it>P </it>= 0.02), and living in a house with soil floors (OR = 3.10; 95% CI: 1.22-7.88; <it>P </it>= 0.01), whereas <it>Toxoplasma </it>infection was negatively associated with traveling abroad (OR = 0.28; 95% CI: 0.12-0.67; <it>P </it>= 0.005).</p> <p>Conclusions</p> <p>This is the first report of seroprevalence and contributing factors for <it>Toxoplasma </it>infection in workers occupationally exposed to unwashed raw fruits and vegetables, and the results may help in the design of optimal preventive measures against <it>Toxoplasma </it>infection especially in female workers at reproductive age.</p

Gradings on Algebras over Algebraically Closed Fields

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