Abstract Hatred: Yeats and the Counter-Revolutionary Paradigm

This article examines W.B. Yeats's affiliation to a counter-revolutionary tradition that had its origins in the works of Edmund Burke and incorporated a range of later writers from Alexis de Tocqueville to Hippolyte Taine. This tradition possesses significant internal differences and contradictions, but it derives its general structure and coherence from a shared distrust of particular kinds of theoretical abstraction. Placed against this background, Yeats's extravagant campaign against the abstract develops political substance and form. The article demonstrates how Yeats's general denunciation of abstraction in politics drives his attacks on both nationalism and democracy in Ireland.

Reduced K-theory for Azumaya algebras

Abstract In the theory of central simple algebras, often we are dealing with abelian groups which arise from the kernel or co-kernel of functors which respect transfer maps (for example K-functors). Since a central simple algebra splits and the functors above are “trivial” in the split case, one can prove certain calculus on these functors. The common examples are kernel or co-kernel of the maps Ki(F)?Ki(D), where Ki are Quillen K-groups, D is a division algebra and F its center, or the homotopy fiber arising from the long exact sequence of above map, or the reduced Whitehead group SK1. In this note we introduce an abstract functor over the category of Azumaya algebras which covers all the functors mentioned above and prove the usual calculus for it. This, for example, immediately shows that K-theory of an Azumaya algebra over a local ring is “almost” the same as K-theory of the base ring. The main result is to prove that reduced K-theory of an Azumaya algebra over a Henselian ring coincides with reduced K-theory of its residue central simple algebra. The note ends with some calculation trying to determine the homotopy fibers mentioned above.

K1 of Chevalley groups are nilpotent

Abstract Let F be a reduced irreducible root system and R be a commutative ring. Further, let G(F,R) be a Chevalley group of type F over R and E(F,R) be its elementary subgroup. We prove that if the rank of F is at least 2 and the Bass-Serre dimension of R is finite, then the quotient G(F,R)/E(F,R) is nilpotent by abelian. In particular, when G(F,R) is simply connected the quotient K1(F,R)=G(F,R)/E(F,R) is nilpotent. This result was previously established by Bak for the series A1 and by Hazrat for C1 and D1. As in the above papers we use the localisation-completion method of Bak, with some technical simplifications.

Social economy and economic crisis in the basque country abstract

This article examines the socio-economic evolution of the social economy sector in the Basque Country during the 2008-2014 period of economic crisis. Data have been obtained within a framework of collaboration between university, Basque Government and private sector of the social economy. The results suggest that such entities have evolved better, both in terms of number of enterprises and employment, than the general economy of the Basque Country, while the context of public policies aimed at social economy has worsened over the years. However, in economic terms (measured through the Gross Value Added generated), they have not been able to cope with the crisis in equal conditions to the general economy. The main contribution of this research lies in that, unlike similar studies, it discusses the evolution of the whole sector of the social economy, taking as reference a broad period of the current economic crisis.