Dilations of partial representations of Hopf algebras

We introduce the notion of a dilation for a partial representation (i.e. a partial module) of a Hopf algebra, which in case the partial representation origins from a partial action (i.e.a partial module algebra) coincides with the enveloping action (or globalization). This construction leads to categorical equivalences between the category of partial $H$-modules, a category of (global) $H$-modules endowed with a projection satisfying a suitable commutation relation and the category of modules over a (global) smash product constructed upon $H$, from which we deduce the structure of a Hopfish algebra on this smash product. These equivalences are used to study the interactions between partial and global representation theory.Comment: 25 pages. Corrected several typos, final version to appear in Journal of the London Mathematical Societ

Do desenvolvimento do software livre à produção colaborativa em massa

TCC (graduação) - Universidade Federal de Santa Catarina. Centro Sócio-Econômico. Economia.Este trabalho não possui resumo

THE OPTIMIZATION OF A TIME-RESOLVED, VESICLE-BASED FLUORESCENCE ASSAY FOR THE ACTIVITY OF THE LIPID KINASE PI4K-IIIBETA AND THE EFFECT OF LIPID TRANSFER PROTEINS ON ENZYME ACTIVITY

Human PI4K-IIIβ is an 89 kDa phosphatidylinositol (PI) kinase that phosphorylates its substrate headgroup at position C-4, thus producing PI(4)P. This phosphoinositide is the most abundant in the trans-Golgi network where it is essential for secretory vesicle formation, as well as the precursor for other phosphoinositides that are crucial for intracellular signalling. Among others, phosphoinositide homeostasis in eukaryotic membranes rely on PI kinases and PI transfer proteins (PITPs). In yeast, the PITP Sec14p is known to exchange PI and phosphatidylcholine between lipid bilayers in vitro and proposed to present PI to be phosphorylated by the PI4-kinase Pik1 in a heterotypic ligand exchange fashion. However, the precise mechanism by which this interaction occurs has yet to be elucidated. To explore how and if PITPs and PI4K-IIIβ work as hypothesized, we expressed and purified recombinant human PI4K-IIIβ in Escherichia coli and assayed lipid kinase activity using an optimized real-time, vesicle-based fluorescence assay. After comparing different affinity tags, deletion mutants and expressing cell lines, GST-tagged wild-type PI4K-IIIβ was chosen and expressed in Rosetta 2(DE3) cells with a 2.5-fold increase in the native protein yield when compared to other methods. Proteins were further purified by an addition heat shock protein removal wash. The resulting PI4K-IIIβ displayed activity comparable to the commercially available, insect cell expressed counterpart. Optimization of the activity assay afforded a robust assay that displayed protein concentration dependent response while using unilamellar liposomes as the substrate. Agreeing with previous reports, the activity of PI4K-IIIβ was greatly reduced by wortmannin and increased by Triton X-100. The activity of PI4K-IIIβ was tested in the presence of active human PITPα and PITPβ, as well as yeast Frequenin and Sec14p, but none of them elicited a reproducible enhancement on PI(4)P production by PI4K-IIIβ. A similar pattern was observed with the human PI3-kinase, PIK3C3. Our results demonstrate that a PI presentation model based on heterotypic exchange may not occur in vitro, suggesting either that PITPs’ role in phosphoinositide production could rely uniquely on maintaining sufficient PI pools in the Golgi membrane or that additional protein partners may be required for the regulation of PI4K-IIIβ by PITPs

Error-block codes and poset metrics

Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is constant on the non-null vectors of a component V-i, extending both the poset metric introduced by Brualdi et al. and the metric for linear error-block codes introduced by Feng et al.. We classify all poset block structures which admit the extended binary Hamming code [8; 4; 4] to be a one-perfect poset block code, and present poset block structures that turn other extended Hamming codes and the extended Golay code [24; 12; 8] into perfect codes. We also give a complete description of the groups of linear isometrics of these metric spaces in terms of a semi-direct product, which turns out to be similar to the case of poset metric spaces. In particular, we obtain the group of linear isometrics of the error-block metric spaces.Let P = ({1, 2,..., n}, <=) be a poset, let V-1, V-2,...,V-n, be a family of finite-dimensional spaces over a finite field F-q and let V = V-1 circle plus V-2 circle plus ... V-n. In this paper we endow V with a poset metric such that the P-weight is cons2195111FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçã

Symmetry groups of Rosenbloom-Tsfasman spaces

Let F(q)(m.n) he the vector space of m . n-tuples over a finite field Fit and P = {1, 2,..., m - n} a poset that is the finite union of In disjoint chains of length it. We consider on F(q)(m.n) the poset-metric d(p) introduced by Rosenbloom and Tsfasman. In this paper, we give a complete description of the symmetry group of the metric space (V, d(p)). (C) 2008 Elsevier B.V. All rights reserved.Let F(q)(m.n) he the vector space of m . n-tuples over a finite field Fit and P = {1, 2,..., m - n} a poset that is the finite union of In disjoint chains of length it. We consider on F(q)(m.n) the poset-metric d(p) introduced by Rosenbloom and Tsfasman.3094763771FAPESP - FUNDAÇÃO DE AMPARO À PESQUISA DO ESTADO DE SÃO PAULOsem informaçãoThe authors would like to thank the anonymous referee for valuable remarks which led to sensible improvements in the text and in the proof