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2. On split liftings with sectional complementsAleksander Malnič, Rok Požar, 2018, original scientific article Keywords: algorithm, Cayley voltages, covering projection, graph, group presentation, invariant section, lifting automorphisms, linear systems over the integers, split extension Published in RUP: 02.03.2018; Views: 2355; Downloads: 175 Link to full text |
3. On the split structure of lifted groupsAleksander 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 Full text (422,56 KB) |
4. A rhizome as a map of a rupture of the cartesian dualismKatja 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 Link to full text |
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