The Politics of Abstract Art. Forma 1 and the Italian Communist Party

Este artículo examina el papel del grupo de artistas abstractos Forma 1 en relación con la política cultural del Partido Comunista Italiano durante la posguerra, como ejemplo de los intentos de superar la dicotomía establecida en Italia entre arte abstracto y realismo socialista y producir una alternativa a la confrontación entre ambos discursos estéticos. Mientras los artistas realistas socialistas subrayaban la necesidad de expresar contenidos políticos explícitos con un estilo que asegurase su máxima legibilidad para una audiencia de masas, los artistas de Forma 1 argumentaban que la abstracción significaba una crítica de la representación pictórica que podía contribuir a la crítica de la ideología burguesa, armonizando de este modo el marxismo con los desarrollos artísticos más avanzados. El PCI, por su parte, basaba su política artística en amplias alianzas de artistas e intelectuales antifascistas, que cada vez eran más difíciles de mantener en el clima de creciente confrontación política y cultural que siguió a la II Guerra Mundial

Twisted equivariant K-theory of compact Lie group actions with maximal rank isotropy

We consider twisted equivariant K--theory for actions of a compact Lie group $G$ on a space $X$ where all the isotropy subgroups are connected and of maximal rank. We show that the associated rational spectral sequence \`a la Segal has a simple $E_2$--term expressible as invariants under the Weyl group of $G$. Namely, if $T$ is a maximal torus of $G$, they are invariants of the $\pi_1(X^T)$-equivariant Bredon cohomology of the universal cover of $X^T$ with suitable coefficients. In the case of the inertia stack $\Lambda Y$ this term can be expressed using the cohomology of $Y^T$ and algebraic invariants associated to the Lie group and the twisting. A number of calculations are provided. In particular, we recover the rational Verlinde algebra when $Y=\{*\}$.Comment: To appear in Journal of Mathematical Physics. Some mistakes have been corrected in Section

Serial coalgebras and their valued Gabriel quivers

We study serial coalgebras by means of their valued Gabriel quivers. In particular, Hom-computable and representation-directed coalgebras are characterized. The Auslander-Reiten quiver of a serial coalgebra is described. Finally, a version of Eisenbud-Griffith theorem is proved, namely, every subcoalgebra of a prime, hereditary and strictly quasi-finite coalgebra is serial.Comment: 22 page

Equivariant K-theory of compact Lie group actions with maximal rank isotropy

Let G denote a compact connected Lie group with torsion-free fundamental group acting on a compact space X such that all the isotropy subgroups are connected subgroups of maximal rank. Let $T\subset G$ be a maximal torus with Weyl group W. If the fixed-point set $X^T$ has the homotopy type of a finite W-CW complex, we prove that the rationalized complex equivariant K-theory of X is a free module over the representation ring of G. Given additional conditions on the W-action on the fixed-point set $X^T$ we show that the equivariant K-theory of X is free over R(G). We use this to provide computations for a number of examples, including the ordered n-tuples of commuting elements in G with the conjugation action.Comment: Accepted for publication by the Journal of Topolog