If A is a fixed abelian group with endomorphism ring E, then for any group G, ลฝ . ลฝ . let G\* s Hom G, A and for any E-module M, let M\* s Hom M, A . The E evaluation map : G ยช G\*\* is defined in the usual way and G is A-reflexive if G is an isomorphism. This is strongly related to the question of
Dualities for Locally Completely Decomposable Abelian Groups
โ Scribed by C. Vinsonhaler; W. Wickless
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 310 KB
- Volume
- 191
- Category
- Article
- ISSN
- 0021-8693
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๐ SIMILAR VOLUMES
when A is a torsion-free abelian group of rank one. As a consequence he was able to show that a finite rank torsion-free group M satisfies M ( nat M\*\* if and only if M F A I and pM s M precisely when pA s A, where ลฝ . M\*sHom y, A . Using this Warfield obtained a characterization of Z ลฝ . w x the
Semisimple tensor categories with fusion rules of self-duality for finite abelian groups are classified. As an application, we prove that the Tannaka duals of the dihedral and the quaternion groups of order 8 and the eight-dimensional Hopf algebra of Kac and Paljutkin are not isomorphic as abstract