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On the split structure of lifted groups
Aleksander Malnič, Rok Požar, 2016, original scientific article

Abstract: Let ▫$\wp \colon \tilde{X} \to X$▫ be a regular covering projection of connected graphs with the group of covering transformations ▫$\rm{CT}_\wp$▫ being abelian. Assuming that a group of automorphisms ▫$G \le \rm{Aut} X$▫ lifts along $\wp$ to a group ▫$\tilde{G} \le \rm{Aut} \tilde{X}$▫, the problem whether the corresponding exact sequence ▫$\rm{id} \to \rm{CT}_\wp \to \tilde{G} \to G \to \rm{id}$▫ splits is analyzed in detail in terms of a Cayley voltage assignment that reconstructs the projection up to equivalence. In the above combinatorial setting the extension is given only implicitly: neither ▫$\tilde{G}$▫ nor the action ▫$G\to \rm{Aut} \rm{CT}_\wp$▫ nor a 2-cocycle ▫$G \times G \to \rm{CT}_\wp$▫, are given. Explicitly constructing the cover ▫$\tilde{X}$▫ together with ▫$\rm{CT}_\wp$▫ and ▫$\tilde{G}$▫ as permutation groups on ▫$\tilde{X}$▫ is time and space consuming whenever ▫$\rm{CT}_\wp$▫ is large; thus, using the implemented algorithms (for instance, HasComplement in Magma) is far from optimal. Instead, we show that the minimal required information about the action and the 2-cocycle can be effectively decoded directly from voltages (without explicitly constructing the cover and the lifted group); one could then use the standard method by reducing the problem to solving a linear system of equations over the integers. However, along these lines we here take a slightly different approach which even does not require any knowledge of cohomology. Time and space complexity are formally analyzed whenever ▫$\rm{CT}_\wp$▫ is elementary abelian.
Keywords: algorithm, abelian cover, Cayley voltages, covering projection, graph, group extension, group presentation, lifting automorphisms, linear systems over the integers, semidirect product
Published in RUP: 15.10.2015; Views: 2675; Downloads: 157
.pdf Full text (422,56 KB)

4.
A rhizome as a map of a rupture of the cartesian dualism
Katja Cergolj Edwards, 2008, original scientific article

Abstract: This essay explores the potentiality of organizing the immediate reality of lived experience of modern individual through a construct of Deleuze' and Guattari's rhizome. This practice, claimed in this essay, negates the traditional construction of knowledge, based on Cartesian perspectivalism, and offers nomadic identities of postcolonial world prospective of active, performative construction of personal bricolages
Keywords: postcolonialism, dualism, identity, cartesian, rhizome, re-presentation, multiplicity, nomadism, performativity
Published in RUP: 10.07.2015; Views: 2237; Downloads: 33
URL Link to full text

5.
Classification of prosthetic joint infections
Rihard Trebše, Anže Mihelič, 2012, independent scientific component part or a chapter in a monograph

Keywords: classification, infections, symptoms, presentation
Published in RUP: 15.10.2013; Views: 3232; Downloads: 136
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6.
Urban archaeology of Koper/Capodistria
Zrinka Mileusnić, 2011, published scientific conference contribution

Keywords: urban archaeology, interpretation, presentation, Koper
Published in RUP: 15.10.2013; Views: 2918; Downloads: 31
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