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The tensor structure on the representation category of the triplet algebra
We study the braided monoidal structure that the fusion product induces on
the abelian category -mod, the category of representations of
the triplet -algebra . The -algebras are a
family of vertex operator algebras that form the simplest known examples of
symmetry algebras of logarithmic conformal field theories. We formalise the
methods for computing fusion products, developed by Nahm, Gaberdiel and Kausch,
that are widely used in the physics literature and illustrate a systematic
approach to calculating fusion products in non-semi-simple representation
categories. We apply these methods to the braided monoidal structure of
-mod, previously constructed by Huang, Lepowsky and Zhang, to
prove that this braided monoidal structure is rigid. The rigidity of
-mod allows us to prove explicit formulae for the fusion product
on the set of all simple and all projective -modules, which were
first conjectured by Fuchs, Hwang, Semikhatov and Tipunin; and Gaberdiel and
Runkel.Comment: 58 pages; edit: added references and revisions according to referee
reports. Version to appear on J. Phys.
Labor unions and corporate cash holdings: evidence from international data
This is the author accepted manuscript. The final version is available from Wiley via the DOI in this record.Firms in countries with higher union membership have less corporate cash holdings. This negative relation is stronger for firms in countries with weak employment protection legislation, firms in countries with a high degree of labor bargaining centralization, and financially constrained firms. Moreover, the market value of corporate cash holdings is lower for firms in countries with high union membership. The number of strikes and lockouts is higher in countries with more corporate cash holdings. We conclude that firms strategically choose corporate cash holdings to gain a bargaining position with labor in an international setting
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