On the quiver of the descent algebra

We study the quiver of the descent algebra of a finite Coxeter group W. The results include a derivation of the quiver of the descent algebra of types A and B. Our approach is to study the descent algebra as an algebra constructed from the reflection arrangement associated to W.Comment: 31 pages, LaTeX; major revision; to appear in Journal of Algebr

Changing perspectives on the internationalization of R&D and innovation by multinational enterprises: a review of the literature

Internationalization of R&D and innovation by Multinational Enterprises (MNEs) has undergone a gradual and comprehensive change in perspective over the past 50 years. From sporadic works in the late 1950s and in the 1960s, it became a systematically analysed topic in the 1970s, starting with pioneering reports and “foundation texts”. Our review unfolds the theoretical and empirical evolution of the literature from dyadic interpretations of centralization versus decentralization of R&D by MNEs to more comprehensive frameworks, wherein established MNEs from Advanced Economies still play a pivotal role, but new players and places also emerge in the global generation and diffusion of knowledge. Hence views of R&D internationalization increasingly rely on concepts, ideas and methods from IB and other related disciplines such as industrial organization, international economics and economic geography. Two main findings are highlighted. First, scholarly research pays an increasing attention to the network-like characteristics of international R&D activities. Second, different streams of literature have emphasized the role of location- specific factors in R&D internationalization. The increasing emphasis on these aspects has created new research opportunities in some key areas, including inter alia: cross-border knowledge sourcing strategies, changes in the geography of R&D and innovation, and the international fragmentation of production and R&D activities

The face semigroup algebra of a hyperplane arrangement

This article presents a study of an algebra spanned by the faces of a hyperplane arrangement. The quiver with relations of the algebra is computed and the algebra is shown to be a Koszul algebra. It is shown that the algebra depends only on the intersection lattice of the hyperplane arrangement. A complete system of primitive orthogonal idempotents for the algebra is constructed and other algebraic structure is determined including: a description of the projective indecomposable modules, the Cartan invariants, projective resolutions of the simple modules, the Hochschild homology and cohomology, and the Koszul dual algebra. A new cohomology construction on posets is introduced, and it is shown that the face semigroup algebra is isomorphic to the cohomology algebra when this construction is applied to the intersection lattice of the hyperplane arrangement

RESEARCH STATEMENT

My research interests fall under the broad categories of algebraic combinatorics and discrete geometry. I am especially interested in the interplay between algebra, combinatorics and representation theory. The following sections provide an overview of my main research projects, a description of my results and an outline of my future research plans