29,103 research outputs found

    Quivers and Three-Dimensional Lie Algebras

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    We study a family of three-dimensional Lie algebras LμL_\mu that depend on a continuous parameter μ\mu. We introduce certain quivers, which we denote by Qm,nQ_{m,n} (m,nZ)(m,n \in \mathbb{Z}) and Q×Q_{\infty \times \infty}, and prove that idempotented versions of the enveloping algebras of the Lie algebras LμL_{\mu} are isomorphic to the path algebras of these quivers modulo certain ideals in the case that μ\mu is rational and non-rational, respectively. We then show how the representation theory of the quivers Qm,nQ_{m,n} and Q×Q_{\infty\times\infty} can be related to the representation theory of quivers of affine type AA, and use this relationship to study representations of the Lie algebras LμL_\mu. In particular, though it is known that the Lie algebras LμL_\mu are of wild representation type, we show that if we impose certain restrictions on weight decompositions, we obtain full subcategories of the category of representations of LμL_\mu that are of finite or tame representation type.Comment: 18 page

    Destination Branding - Tracking Brand Equity for a Competitive Set of Near-Home Destinations

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    In the emerging literature related to destination branding, little has been reported about performance metrics. The focus of most research reported to date has been concerned with the development of destination brand identities and the implementation of campaigns (see for example, Crockett & Wood 1999, Hall 1999, May 2001, Morgan et al 2002). One area requiring increased attention is that of tracking the performance of destination brands over time. This is an important gap in the tourism literature, given: i) the increasing level of investment by destination marketing organisations (DMO) in branding since the 1990s, ii) the complex political nature of DMO brand decision-making and increasing accountability to stakeholders (see Pike, 2005), and iii) the long-term nature of repositioning a destination’s image in the market place (see Gartner & Hunt, 1987). Indeed, a number of researchers in various parts of the world have pointed to a lack of market research monitoring destination marketing objectives, such as in Australia (see Prosser et. al 2000, Carson, Beattie and Gove 2003), North America (Sheehan & Ritchie 1997, Masberg 1999), and Europe (Dolnicar & Schoesser 2003)..

    The active aging agenda, old folk devils and a new moral panic

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    The proposal that older people should engage in “active aging” has come to dominate local, national, and international policy agendas. This encompasses a variety of ways that older persons might maintain active citizenship, but invariably promotes physical activity and exercise as having health and social benefits, despite a lack of conclusive evidence to support such claims. In this paper, I further examine the meaning of these claims through an analysis of policy documents, reports, and media articles which promote the perceived benefits of physical activity in later life. I revisit Cohen’s (2002) concepts of folk devils and moral panics to understand how these messages simultaneously problematize older people while creating a market for emergent moral entrepreneurs who claim to have the solution to the problem they have in part created. I conclude with recommendations for improved understanding of the benefits and appropriate provision for active aging.</jats:p

    Tourism Destination Branding Complexity

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    Prior to completing a tourism marketing PhD the author spent almost two decades working in the tourism industry, mostly in destination marketing organisations (DMOs). In this paper he laments a significant gap in the literature in the area of tourism destination branding, a field that has only attracted academic attention since the late 1990s. While interest in applications of brand theory to practise in tourism is increasing, there is a paucity of published research with which to guide DMOs. There has been relatively little discussion on the complexity involved in capturing the essence of a multi-attributed destination with a succinct and focused brand position, in a way that is both meaningful to the multiplicity of target audiences of interest to stakeholders and effectively differentiates the destination from competitors. The paper summarises six issues that make the application of branding theory to destinations a complex undertaking

    Therapeutic Use Exemptions and the Doctrine of Double Effect

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    Without taking a position on the overall justification of anti-doping regulations, I analyse the possible justification of Therapeutic Use Exemptions (TUEs) from such rules. TUEs are a creative way to prevent the unfair exclusion of athletes with a chronic condition, and they have the potential to be the least bad option. But they cannot be competitively neutral. Their justification must rest, instead, on the relevance of intentions to permissibility. I illustrate this by means of a set of thought experiments in which only an athlete’s intentions vary. I argue that the Doctrine of Double Effect (DDE) sheds some light on TUEs and illustrate this by applying different readings of the DDE to the thought experiment. This underpins a justification of anti-doping exemptions very different from the approach adopted by the World Anti-Doping Agency (WADA). I argue for three changes to bring TUEs in line with this understanding: rewriting of the regulations, transparency, and a greater role for athletes in determining what exemptions are allowed, and when

    Additive relative invariants and the components of a linear free divisor

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    A 'prehomogeneous vector space' is a rational representation ρ:GGL(V)\rho:G\to\mathrm{GL}(V) of a connected complex linear algebraic group GG that has a Zariski open orbit ΩV\Omega\subset V. Mikio Sato showed that the hypersurface components of D:=VΩD:=V\setminus \Omega are related to the rational characters HGL(C)H\to\mathrm{GL}(\mathbb{C}) of HH, an algebraic abelian quotient of GG. Mimicking this work, we investigate the 'additive functions' of HH, the homomorphisms Φ:H(C,+)\Phi:H\to (\mathbb{C},+). Each such Φ\Phi is related to an 'additive relative invariant', a rational function hh on VV such that hρ(g)h=Φ(g)h\circ \rho(g)-h=\Phi(g) on Ω\Omega for all gGg\in G. Such an hh is homogeneous of degree 00, and helps describe the behavior of certain subsets of DD under the GG--action. For those prehomogeneous vector spaces with DD a type of hypersurface called a linear free divisor, we prove there are no nontrivial additive functions of HH, and hence HH is an algebraic torus. From this we gain insight into the structure of such representations and prove that the number of irreducible components of DD equals the dimension of the abelianization of GG. For some special cases (GG abelian, reductive, or solvable, or DD irreducible) we simplify proofs of existing results. We also examine the homotopy groups of VDV\setminus D.Comment: 27 pages. From v1, strengthen results in section 3, improve prose, and update contact informatio
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