Examples of finite-dimensional Hopf algebras with the dual Chevalley property

We present new Hopf algebras with the dual Chevalley property by determining all semisimple Hopf algebras Morita-equivalent to a group algebra over a finite group, for a list of groups supporting a non-trivial finite-dimensional Nichols algebra.Comment: Final version. Accepted for publication in Publicacions Matem\`atique

Ejemplos de álgebras de Hopf semisimples y de álgebras de Hopf con la propiedad de Chevalley dual

Tesis (Doctor en Matemática)--Universidad Nacional de Córdoba, Facultad de Matemática, Astronomía, Física y Computación, 2016.En la primera parte de esta tesis, damos ejemplos, y planteamos algunas preguntas, sobre extensiones de álgebras de Hopf semisimples. Para esto, definimos la noción de longitud de un álgebra de Hopf, por ejemplo, que un álgebra de Hopf H sea de longitud 1 significa que H es simple; de longitud 2, que H es una extensión de T por K, donde K y T son álgebras de Hopf simples. Presentamos ejemplos de álgebras de Hopf de longitud 2 que no son extensiones abelianas. En la segunda parte, presentamos ejemplos de álgebras de Hopf con la propiedad de Chevalley dual, o sea, álgebras de Hopf cuyo corradical es una subálgebra de Hopf. Para esto, determinamos todas las álgebras de Hopf semisimples Morita-equivalentes a un álgebra de grupo de un grupo finito, para una lista de grupos que soportan álgebras de Nichols no-triviales de dimensión finita.In the first part of this thesis, we give some examples of, and raise some questions on, extensions of semisimple Hopf algebras. For this, we define the notion of length of a Hopf algebra, for example, a Hopf algebra H has length 1 means that H is simple; of length 2, that H is an extension of T by K, where T and K are simple Hopf algebras. We present examples of Hopf algebras of length 2 that are not abelian extensions. In the second part, we present examples of Hopf algebras with the dual Chevalley property, that is, an Hopf algebra whose coradical is a Hopf subalgebra. For this, we determine all semisimple Hopf algebras Morita-equivalent to a group algebra over a finite group, for a list of groups supporting a non-trivial finite-dimensional Nichols algebra

Ejemplos de extensiones de álgebras de Hopf

We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras.Damos algunos ejemplos de, y planteamos algunas preguntas sobre, extensiones de álgebras de Hopf semisimples.https://revistas.unal.edu.co/index.php/recolma/article/view/54180publishedVersionFil: Andruskiewitsch, Nicolás. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Fil: Müller Lopes Rocha, Monique. Universidad Nacional de Córdoba. Facultad de Matemática, Astronomía y Física; Argentina.Matemática Pur

Family Group Conference (FGC) und Täter-Opfer-Ausgleich (TOA) : Restorative Justice in Neuseeland und in Deutschland

Das deutsche Jugendstrafrechtssystem wird trotz wiederholter Änderungen des Jugendgerichtsgesetzes und den Bemühungen zu einer auch kriminalpräventiv wirkenden Umsetzung in der Praxis immer wieder kritisiert. Über die Frage, wie eine nachhaltige Reform des Jugendstrafrechts auszusehen hätte, wird immer wieder diskutiert. Die meisten Kriminologen und Praktiker plädieren für die vermehrte Anwendung von Mediation und ambulanten Maßnahmen. Ziel dieser Arbeit ist es, einen Beitrag zu dieser Diskussion durch Vergleich mit ausländischen Regelungen – im Speziellen mit dem neuseeländischen Jugendstrafrecht - zu leisten. Dabei wird insbesondere die im neuseeländischen Jugendstrafrecht eingeführte Family Group Conference (FGC) beleuchtet und mit dem in Deutschland existierenden Täter-Opfer-Ausgleich (TOA) verglichen. Hintergrund dafür war, dass das frühere neuseeländische Jugendstrafrecht im Kern derselben Kritik wie das geltende deutsche Jugendstrafrecht ausgesetzt war. Mit dieser Arbeit soll daher untersucht werden, ob das neuseeländische Jugendstrafrechtssystem auch in jüngerer Zeit noch grundsätzlich als erfolgversprechend bewertet werden kann. Bejahendenfalls soll sodann untersucht werden, ob und ggf. mit welchen Anpassungen an die deutsche Rechtslage die FGC auch als eine (ergänzende) Alternative zu den überkommenen Reaktionsformen des deutschen Jugendstrafrechtssystems in Betracht zu ziehen wäre

Psychiatric characterization of children with genetic causes of hyperandrogenism

Objective: Very little is known about the mental health status in children with genetic causes of hyperandrogenism. This study sought to characterize psychiatric morbidity in this group. Design/methods: Children (8-18 years) with the diagnosis of classic congenital adrenal hyperplasia (CAH) or familial male precocious puberty (FMPP) underwent a semi-structured psychiatric interview, the Kiddie Schedule for Affective Disorders and Schizophrenia-Present and Lifetime Version. According to sex and the literature, incidence of identified psychopathology was compared between the two endocrinological groups. We evaluated 72 patients: 54 CAH (21 females) and 18 FMPP. Results: Twenty-four (44.4%) CAH patients and 10 (55.6%) FMPP patients met the criteria for at least one lifetime psychiatric diagnosis. Attention-deficit hyperactivity disorder (ADHD) was present in 18.2% of CAH males, 44.4% of FMPP males, and one case (4.8%) in CAH females. A high rate of anxiety disorders was also found in all the three groups (17-21%). Relative to females with CAH, the FMPP patients exhibited higher rates of ADHD. Age at diagnosis and the treatment modalities were not associated with psychopathology. Rates of psychiatric disorder, specifically ADHD and anxiety disorders, were higher than in the general population. Conclusion: Although anxiety disorders may occur at an increased rate in children with chronic illness, androgens may contribute to higher risk for psychopathology in pediatric patients with genetic cause of excess androgen. Early diagnosis and treatment of childhood hyperandrogenism is essential for optimal development. The results suggest that assessment for psychiatric disorders should be part of the routine evaluation of these patients

Maurer-Cartan equation for gentle algebras

Let $A= \Bbbk Q/I$ be a finite-dimensional gentle algebra. In this article, under some hypothesis on the quiver $Q$, we give conditions for nilpotency of the $L_\infty$-structure on the shifted Bardzell's complex $B(A)[1]$. For nilpotent cases, we describe Maurer-Cartan elements.Comment: 26 page

Ejemplos de extensiones de álgebras de Hopf

Damos algunos ejemplos de, y planteamos algunas preguntas sobre, extensiones de álgebras de Hopf semisimples.We give some examples of, and raise some questions on, extensions of semisimple Hopf algebras

Sobre coálgebras distributivas e de cadeia

Dissertação (mestrado) - Universidade Federal de Santa Catarina, Centro de Ciências Físicas e Matemáticas, Programa de Pós-graduação em Matemática e Computação Científica, Florianópolis, 2010O conceito de distributividade em anéis e módulos vem sendo estudado desde a década de 70, veja por exemplo [11]. Em [8] Lomp e Sant'Ana obtiveram resultados a respeito da distributividade no reticulado dos subcomódulos de uma coálgebra, vista como um comódulo sobre si mesma, a partir de resultados sobre a distributividade em anéis e módulos. Com base nesse artigo, temos o que segue. Seja C uma coálgebra sobre um corpo k. Dizemos que C é uma coálgebra distributiva à direita se o reticulado dos coideais à direita de C é distributivo. Neste trabalho mostraremos que isto é equivalente à dizer que C é uma coálgebra distributiva à esquerda, isto é, o reticulado dos coideais à esquerda de C é distributivo. Portanto, uma coálgebra é dita distributiva se é distributiva à direita ou à esquerda. Nosso principal objetivo é caracterizar coálgebras distributivas em termos de coálgebras de cadeia à direita, que são coálgebras em que o reticulado dos coideais à direita é totalmente ordenado por inclusão

Grey matter volume in adolescent anxiety: an impact of the Brain-derived neurotropic factor Val66Met polymorphism?

Objective: Minimal research links anxiety disorders in adolescents to regional gray matter volume (GMV) abnormalities and their modulation by genetic factors. Prior research suggests that a brain-derived neurotrophic factor (BNDF) Val(66)Met polymorphism may modulate such brain morphometry profiles. Method: Using voxel-based morphometry and magnetic resonance imaging, associations of BDNF and clinical anxiety with regional GMVs of anterior cingulate cortex, insula, amygdala, and hippocampus were examined in 39 affected (17 Met allele carriers, 22 Val/Val homozygotes) and 63 nonaffected adolescents (33 Met allele carriers, 41 Val/Val homozygotes). Results: Amygdala and anterior hippocampal GMVs were significantly smaller in patients than in healthy comparison adolescents, with a reverse pattern for the insula. Post-hoc regression analyses indicated a specific contribution of social phobia to the GMV reductions in the amygdala and hippocampus. In addition, insula and dorsal anterior cingulate cortex (ACC) GMVs were modulated by BDNF genotype. In both regions, and GMVs were larger in the Val/Val homozygote patients than in individuals carrying the Met allele. Conclusions: These results implicate reduced GMV in the amygdala and hippocampus in pediatric anxiety, particularly social phobia. In addition, the data suggest that genetic factors may modulate differences in the insula and dorsal ACC. J. Am. Acad. Child Adolesc. Psychiatry; 2013;52(2):184-195

Stated Preferences of Physicians and Chronic Pain Sufferers in the Use of Classic Strong Opioids

AbstractWe conducted a two-stage study in France, Germany, Italy, Spain, Sweden, and the United Kingdom of the stated preferences of chronic pain sufferers treated with classic strong opioids and of physicians treating such patients. The qualitative stage identified attributes perceived important through focus groups with 84 pain sufferers and semistructured interviews with 11 physicians. The quantitative stage included online, discrete choice experiments (DCEs) in which respondents chose between hypothetical profiles or an opt-out in 15 choice tasks. The profile descriptions were based on the attributes elicited in the qualitative stage. DCEs were conducted for pain sufferers (N = 242) and physicians (N = 270) who passed a rationality test. Main-effects models were estimated by hierarchical Bayesian regression. Sufferers ranked nausea, pain impact, energy, alertness, and constipation; physicians ranked pain response, central nervous system (CNS) effects, nausea, dose form, and constipation in descending order of importance. Sufferers were unwilling to incur severe side effects to decrease pain and chose the opt-out in approximately one half of the choice tasks, whereas physicians were willing to trade between profiles. The models predicted physicians' choices better than those of pain sufferers. No age, sex, or country effects were seen, but stronger preferences were found among physicians treating noncancer (n = 40) than cancer pain and among the 55% of sufferers who had never discontinued long-term pain medication use. Sufferers' mean pain scores on an 11-point Likert scale were 4.0, 5.7, and 8.6 on their best, average, and worst days, respectively