156,791 research outputs found

    Algebras of acyclic cluster type: tree type and type A~\widetilde{A}

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    In this paper, we study algebras of global dimension at most 2 whose generalized cluster category is equivalent to the cluster category of an acyclic quiver which is either a tree or of type A~\widetilde{A}. We are particularly interested in their derived equivalence classification. We prove that each algebra which is cluster equivalent to a tree quiver is derived equivalent to the path algebra of this tree. Then we describe explicitly the algebras of cluster type \A_n for each possible orientation of \A_n. We give an explicit way to read off in which derived equivalence class such an algebra lies, and describe the Auslander-Reiten quiver of its derived category. Together, these results in particular provide a complete classification of algebras which are cluster equivalent to tame acyclic quivers.Comment: v2: 37 pages. Title is changed. A mistake in the previous version is now corrected (see Remark 3.14). Other changes making the paper coherent with the version 2 of 1003.491

    C-sortable words as green mutation sequences

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    Let QQ be an acyclic quiver and s\mathbf{s} be a sequence with elements in the vertex set Q0Q_0. We describe an induced sequence of simple (backward) tilting in the bounded derived category D(Q)\mathcal{D}(Q), starting from the standard heart HQ=modkQ\mathcal{H}_Q=\operatorname{mod}\mathbf{k}Q and ending at another heart Hs\mathcal{H}_\mathbf{s} in D(Q)\mathcal{D}(Q). Then we show that s\mathbf{s} is a green mutation sequence if and only if every heart in this simple tilting sequence is greater than or equal to HQ[1]\mathcal{H}_Q[-1]; it is maximal if and only if Hs=HQ[1]\mathcal{H}_\mathbf{s}=\mathcal{H}_Q[-1]. This provides a categorical way to understand green mutations. Further, fix a Coxeter element cc in the Coxeter group WQW_Q of QQ, which is admissible with respect to the orientation of QQ. We prove that the sequence w~\widetilde{\mathbf{w}} induced by a cc-sortable word w\mathbf{w} is a green mutation sequence. As a consequence, we obtain a bijection between cc-sortable words and finite torsion classes in HQ\mathcal{H}_Q. As byproducts, the interpretations of inversions, descents and cover reflections of a cc-sortable word w\mathbf{w} are given in terms of the combinatorics of green mutations.Comment: Last version, to appear in PLM

    On the Cluster Category of a Marked Surface

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    We study in this paper the cluster category C(S,M) of a marked surface (S,M). We explicitly describe the objects in C(S,M) as direct sums of homotopy classes of curves in (S,M) and one-parameter families related to closed curves in (S,M). Moreover, we describe the Auslander-Reiten structure of the category C(S,M) in geometric terms and show that the objects without self-extensions in C(S,M) correspond to curves in (S,M) without self-intersections. As a consequence, we establish that every rigid indecomposable object is reachable from an initial triangulation.Comment: 33 pages, we add a new corollary 1.6 which shows there is a bijection between triangulations of (S,M) and the cluster-tilting objects of C(S,M), and every rigid indecomposable object is reachable from an initial triangulatio

    Fiercely Real?:Tyra Banks and the making of new media celebrity

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    This paper will examine former supermodel Tyra Banks as a contemporary “celebrity entrepreneur,” focusing on Banks’ recent shift from television persona to multimedia icon within a neoliberal popular culture. I argue that our contemporary new media environment, marked by convergent media texts, self-branding, and interactivity, provides an ideal space for Banks to produce and globally circulate her postfeminist star text. Through her websites, Facebook, and Twitter confessionals, Banks is able to successfully navigate the contradictory discourses that insist female celebrities be both “authentic” selves while maintaining a disciplined, hegemonic femininity that becomes legitimized and naturalized. I conclude that while Banks’ mobilization of a hypervisibility and sense of individual agency generates an authenticity that may resonate with her fans, she remains contained by the neoliberal and postfeminist discourses that allow her to have such a prominent Internet presence. Consequently, this paper serves to raise unexplored questions about the relationship between celebrity culture, postfeminist and neoliberal subjectivities, and new media

    Can You Use it in a Sentence? Defining Talent Management

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    Key Findings The term talent management has escaped a standard definition, and nearly every article written on the topic conclude that the concept of talent management is lacking in terms of definition and theoretical development and there is a comparative lack of empirical evidence on the topic. Perhaps the most salient criticism from researchers is that the use of the term talent management is often little more than a rebranding of a range of typical HR activities. A notable feature of much of the existing literature on talent management is that it continues to focus on practices associated with lifetime careers in corporations, despite the fact that the most profound shift over the past 30-plus years in how organizations manage their workforces has been an increase in dismissals and external hiring at all organizational levels. A definition that is consistent with traditional approaches and captures what academic researchers have been doing under the heading of talent management is as follows: the process through which organizations anticipate and meet their needs for talent in strategic jobs

    Just Words: Understanding the Fullness of the Gospel

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    Author: Preus, Jacob A O. (Jacob Aall Ottesen). Title: Just words. Publisher: St Louis : Concordia Publishing House, 2000