http://blogs.springer.com/alge The official blog of ALGE. Moderated by Editor in Chief Alain Verschoren Fri, 27 Mar 2009 09:20:46 +0000 http://backend.userland.com/rss092 en by Heckenberger, Istvan; Joseph, Anthony Let $\mathfrak{g}$ be a complex semisimple Lie algebra, $\mathfrak{b}$ a Borel subalgebra, and $\mathfrak{h}\subset\mathfrak{b}$ a Cartan subalgebra. Let V be a finite dimensional simple $U(\mathfrak{g})$ module. Based on a principal s-triple (e,h,f) and following work of Kostant, Brylinski (J Amer Math Soc 2(3):517–533, 1989) defined ... http://blogs.springer.com/alge/articles/on-the-left-and-right-brylinski-kostant-filtrations/ by Iovanov, Miodrag Cristian It is well known that the torsion part of any finitely generated module over the formal power series ring K[[X]] is a direct summand. In fact, K[[X]] is an algebra dual to the divided power coalgebra over K and the torsion part of any K[[X]]-module actually ... http://blogs.springer.com/alge/articles/when-does-the-rational-torsion-split-off-for-finitely-generated-modules/ by Böhm, Gabriella; Ştefan, Dragoş In a recent paper (Böhm and Stefan, Commun Math Phys 282:239–286, 2008), we gave a general construction of a para-cocyclic structure on a cosimplex, associated to a so called admissible septuple—consisting of two categories, three functors and two natural transformations, subject to compatibility relations. The ... http://blogs.springer.com/alge/articles/examples-of-para-cocyclic-objects-induced-by-bd-laws/ by Beggs, E. J.; Majid, S. We introduce the notion of ‘bar category’ by which we mean a monoidal category equipped with additional structure formalising the notion of complex conjugation. Examples of our theory include bimodules over a *-algebra, modules over a conventional *-Hopf algebra and modules over a more ... http://blogs.springer.com/alge/articles/bar-categories-and-star-operations/ by DOI: 10.1007/s10468-009-9162-5Online Date: 3/24/2009 Print publication date: 10/1/2009View article on SpringerLink http://blogs.springer.com/alge/articles/noncommutative-rings-and-geometry/ by Ardizzoni, A.; Menini, C. In this paper we introduce the notions of connected, 0-connected and strictly graded coalgebra in the framework of an abelian monoidal category $ \mathcal{M} $ and we investigate the relations between these concepts. We recover several results, involving these notions, which are well known in ... http://blogs.springer.com/alge/articles/some-remarks-on-connected-coalgebras/ by Bican, Ladislav At the beginning of this note the $\mathcal{G}$-covers, $\mathcal{G}$ being a hereditary class of modules, are characterized as that for which the homomorphisms into $\mathcal{G}$-precovers are injective as well as that for which the homomorphisms from $\mathcal{G}$-precovers are surjective. The next part studies the (pre)covers of (relatively) ... http://blogs.springer.com/alge/articles/some-properties-of-precovers-and-covers/ by Darpö, Erik A rotation in a Euclidean space V is an orthogonal map δ ∈ O(V) which acts locally as a plane rotation with some fixed angle a(δ) ∈ [0,π]. We give a classification of all finite-dimensional representations of the real algebra $\mathbb{R}\left\langle X,Y\right\rangle$ that are given by rotations, up to orthogonal isomorphism.DOI: ... http://blogs.springer.com/alge/articles/classification-of-pairs-of-rotations-in-finite-dimensional-euclidean-space/ by Van den Bergh, Michel This is a companion note to “Hochschild cohomology and Atiyah classes” by Damien Calaque and the author. Using elementary methods we compute the Kontsevich weight of a wheel with spokes pointing outward. The result is in terms of modified Bernoulli numbers. The same result had ... http://blogs.springer.com/alge/articles/the-kontsevich-weight-of-a-wheel-with-spokes-pointing-outward/ by Huang, Zhaoyong Let R be a left Noetherian ring, S a right Noetherian ring and R ... http://blogs.springer.com/alge/articles/selforthogonal-modules-with-finite-injective-dimension-iii/