2,456 research outputs found

    Rings containing a field of characteristic zero

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    Open access via the Springer Compact AgreementPeer reviewedPublisher PD

    Modules of constant Jordan type with small non-projective part

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    Massey products in the homology of the loopspace of a pp-completed classifying space : finite groups with cyclic Sylow pp-subgroups

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    Funding Information: The authors are grateful to EPSRC: the second author is supported by EP/P031080/1, which also enabled the first author to visit Warwick. The authors would also like to thank the Isaac Newton Institute for Mathematical Sciences, Cambridge, for providing an opportunity to work on this project during the simultaneous programmes ‘-theory, algebraic cycles and motivic homotopy theory’ and ‘Groups, representations and applications: new perspectives’ (one author was supported by each programme). Open access via CUP agreementPeer reviewedPublisher PD

    The singularity and cosingularity categories of C ∗ B G for groups with cyclic Sylow p-subgroups

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    We construct a differential graded algebra (DGA) modelling certain A∞ algebras associated with a finite group G with cyclic Sylow subgroups, namely H∗BG and H∗ΩBG∧p. We use our construction to investigate the singularity and cosingularity categories of these algebras. We give a complete classification of the indecomposables in these categories, and describe the Auslander--Reiten quiver. The theory applies to Brauer tree algebras in arbitrary characteristic, and we end with an example in characteristic zero coming from the Hecke algebras of symmetric groups

    Complete intersections and mod p cochains

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    We give homotopy invariant definitions corresponding to three well known properties of complete intersections, for the ring, the module theory and the endomorphisms of the residue field, and we investigate them for the mod p cochains on a space, showing that suitable versions of the second and third are equivalent and that the first is stronger. We are particularly interested in classifying spaces of groups, and we give a number of examples. This paper follows on from arXiv:0906.4025 which considered the classical case of a commutative ring and arXiv:0906.3247 which considered the case of rational homotopy theory.Comment: To appear in AG

    Monovalent chiral-at-copper complexes: halide-controlled diastereoselectivity

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    An unusual example of diastereoselectivity has been observed in Cu(κ3-P,C,P′-1)X complexes where 1 is an asymmetric tridentate ligand containing a bicyclic NHC framework and X is a halide. When X is Cl−, the SCu isomer is formed selectively whereas when X = I− the RCu diastereomer is preferred

    Variable coordination of a chiral diphosphine containing an amidinium/NHC group within its backbone: μ-P,P′, κ2-P,P′ and κ3-P,C,P′ coordination modes

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    A diphosphine ligand (1·HPF6), which is a potential precursor to a PCNHCP pincer, with a backbone containing two phenylene groups and a central bicyclic 4-aza-2-azoniabicyclo[3.2.1]oct-2-ene unit has been synthesised and coordinated to Pd(II) and Pt(II) to give trans-[M(κ2-P,P′-1·H)Cl2]PF6 where M = Pd (2) or Pt (3a). Single-crystal structure determinations of 2 and 3a show the complexes to be isostructural with the diphosphine coordinated in a trans-spanning fashion and the amidinium unit being protonated and non-coordinated. 2 and 3a react with CH3I to give the dimers trans-[Pd2(μ-1·H)2I4](PF6)2, 6, and trans-[Pt2(μ-1·H)2I4](PF6)2, 7, as the major products. This bridging mode of coordination of [1·H]+ is also seen in trans-[Rh2(μ-1·H)(1,5-COD)2Cl2]PF6, 4, and [Pt2(μ-κ2-1·H)(dvdms)]PF6, 5. Upon treatment with KOtBu complexes 2 and 3a undergo deprotonation at the amidinium carbon to give trans-[M(κ3-P,C,P′-1)Cl]PF6 where M = Pd (8), and Pt (9). The related trans-[Rh(κ3-P,C,P′-1)(CO)]PF6 (10) is prepared directly from 1·HPF6 and Rh(acac)(CO)2: this and the palladium and platinum complexes 8 and 9 are isolated as isomeric mixtures as a consequence of a conformational isomerism. In situ deprotonation of 1·HPF6 followed by addition of Ag(CF3SO3) gave SAg-[Ag(κ3-P,C,P′-1)(CF3SO3)], 11. Some preliminary studies of the reactivity of 2 and 8 in Suzuki-type reactions are reported and the Pt(0) system has been shown to be an active hydrosilylation catalyst

    Seeing the way: visual sociology and the distance runner's perspective

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    Employing visual and autoethnographic data from a two‐year research project on distance runners, this article seeks to examine the activity of seeing in relation to the activity of distance running. One of its methodological aims is to develop the linkage between visual and autoethnographic data in combining an observation‐based narrative and sociological analysis with photographs. This combination aims to convey to the reader not only some of the specific subcultural knowledge and particular ways of seeing, but also something of the runner's embodied feelings and experience of momentum en route. Via the combination of narrative and photographs we seek a more effective way of communicating just how distance runners see and experience their training terrain. The importance of subjecting mundane everyday practices to detailed sociological analysis has been highlighted by many sociologists, including those of an ethnomethodological perspective. Indeed, without the competence of social actors in accomplishing these mundane, routine understandings and practices, it is argued, there would in fact be no social order
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