63 research outputs found

    A PBW basis for Lusztig's form of untwisted affine quantum groups

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    Let g \mathfrak{g} be an untwisted affine Kac-Moody algebra over the field K K \, , and let Uq(g) U_q(\mathfrak{g}) be the associated quantum enveloping algebra; let Uq(g) \mathfrak{U}_q(g) be the Lusztig's integer form of Uq(g) U_q(\mathfrak{g}) \, , generated by q q -divided powers of Chevalley generators over a suitable subring R R of K(q) K(q) \, . We prove a Poincar\'e-Birkhoff-Witt like theorem for Uq(g) \mathfrak{U}_q(\mathfrak{g}) \, , yielding a basis over R R made of ordered products of q q -divided powers of suitable quantum root vectors.Comment: 22 pages, AMS-TeX C, Version 2.1c. This is the author's final version, corresponding to the printed journal versio

    Finite-dimensional representations of twisted hyper loop algebras

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    We investigate the category of finite-dimensional representations of twisted hyper loop algebras, i.e., the hyperalgebras associated to twisted loop algebras over finite-dimensional simple Lie algebras. The main results are the classification of the irreducible modules, the definition of the universal highest-weight modules, called the Weyl modules, and, under a certain mild restriction on the characteristic of the ground field, a proof that the simple modules and the Weyl modules for the twisted hyper loop algebras are isomorphic to appropriate simple and Weyl modules for the non-twisted hyper loop algebras, respectively, via restriction of the action

    Delivering cognitive analytic consultancy to community mental health teams: Initial practice-based evidence from a multi-site evaluation.

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    Objectives: This study sought to employ the hourglass model to frame the methodological evolution of outcome studies concerning 5-session cognitive analytic consultancy (CAC). Design: Pre-post mixed methods evaluation (study one) and mixed methods case series (study two). Methods: In study one, three sites generated acceptability and pre-post effectiveness outcomes from N = 58 care dyads, supplemented with qualitative interviewing. The client outcome measures included the Clinical Outcomes in Routine Evaluation Outcome Measure, Personality Structure Questionnaire, Work and Social Adjustment Questionnaire, Service Engagement Scale, and the Working Alliance Inventory. Study two was a mixed methods case series (N = 5) using an A/B phase design with a 6-week follow-up. Client outcome measures were the Personality Structure Questionnaire, Clinical Outcomes in Routine Evaluation Outcome Measure, and the Working Alliance Inventory, and the staff outcome measures were the Working Alliance Inventory, Maslach Burnout Inventory, and the Perceived Competence Scale. Results: In study one, the cross-site dropout rate from CAC was 28.40% (the completion rate varied from 58 to 100%) and full CAC attendance rates ranged from 61 to 100%. Significant reductions in client distress were observed at two sites. Qualitative themes highlighted increased awareness and understanding across care dyads. In study two, there was zero dropout and full attendance. Clients were significantly less fragmented, and staff felt significantly more competent and less exhausted. Potential mechanisms of change were the effective process skills of the consultant and that emotionally difficult CAC processes were helpful. Conclusions: Cognitive analytic consultancy appears a promising approach to staff consultation, and testing in a clinical trial is now indicated. Practitioner Points: CAC is a suitable method of consultation for care dyads struggling to work effectively together in CMHTs. Staff feel more competent and clients feel less fragmented following CAC, and the benefits of CAC appear to be maintained over follow-up time. CAC processes can be difficult for care coordinator and client, but this is not an impediment to change

    O paradoxo de Bergson: diferença e holismo na antropologia do Ocidente

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