The Koszul dual of a weakly Koszul module

We study the so-called weakly Koszul modules and characterise their Koszul duals. We show that the (adjusted) associated graded module of a weakly Koszul module exactly determines the homology modules of the Koszul dual. We give an example of a quasi-Koszul module which is not weakly Koszul.Comment: 20 page

On a common generalization of Koszul duality and tilting equivalence

We propose a new definition of Koszulity for graded algebras where the degree zero part has finite global dimension, but is not necessarily semi-simple. The standard Koszul duality theorems hold in this setting. We give an application to algebras arising from multiplicity free blocks of the BGG category $\mathcal O$

On bounds of homological dimensions in Nakayama algebras

Let $A$ be a Nakayama algebra with $n$ simple modules and a simple module $S$ of even projective dimension $m$. Choose $m$ minimal such that a simple $A$-module with projective dimension $2m$ exists, then we show that the global dimension of $A$ is bounded by $n+m-1$. This gives a combined generalisation of results of Gustafson \cite{Gus} and Madsen \cite{Mad}. In \cite{Bro}, Brown proved that the global dimension of quasi-hereditary Nakayama algebras with $n$ simple modules is bounded by $n$. Using our result on the bounds of global dimensions of Nakayama algebras, we give a short new proof of this result and generalise Brown's result from quasi-hereditary to standardly stratified Nakayama algebras, where the global dimension is replaced with the finitistic dimension

Examining the popularity trajectory of outsourcing as a management concept

This paper examines the popularity trajectory of outsourcing as a management concept. The paper shows that while outsourcing is an old management practice that has roots that date back centuries, it did not gain widespread popularity as a modern organizational practice until the 1980s. While the initial outsourcing hype and craze of the late 1980s and early 1990s has waned, outsourcing has shown considerable staying power as a management concept, even in the face of counter-movements such as backsourcing and insourcing. Although the experiences with implementation of outsourcing are mixed, outsourcing remains a widely used management concept. However, the current relatively low satisfaction level among users could influence the future popularity trajectory of the outsourcing concept

Not dead yet: the rise, fall and persistence of the BCG Matrix

The BCG Matrix was introduced almost 50 years ago, and is today considered one of the most iconic strategic planning techniques. Using management fashion theory as a theoretical lens, this paper examines the historical rise, fall and persistence of the BCG Matrix. The analysis highlights the role played by fashion-setting actors (e.g., consultants, business schools and business media) in the rise of the BCG Matrix. However, over time, portfolio planning models such as the BCG Matrix were attacked and discredited by a host of different actors, and gradually fell out of favor. Even though the BCG Matrix has fallen from grace, it is still alive and has left an imprint on management education and practice. Despite being largely discredited in academic circles, many practitioners still view it as an important corporate portfolio planning technique

Quasi-hereditary algebras and generalized Koszul duality

We present an easily applicable sufficient condition for standard Koszul algebras to be Koszul with respect to $\Delta$. If a quasi-hereditary algebra \L is Koszul with respect to $\Delta$, then \L and the Yoneda extension algebra of $\Delta$ are Koszul dual in a sense explained below, implying in particular that their bounded derived categories of finitely generated graded modules are equivalent. We also prove that the extension algebra of $\Delta$ is Koszul in the classical sense.Comment: This is a revised and updated version of the last section of arXiv:1007.328