An isomorphism for the Grothendieck ring of a Hopf algebra order
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- by Anna-Lise Jensen and Richard G. Larson
- Proc. Amer. Math. Soc. 97 (1986), 197-200
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835864-3
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Abstract:
If $G$ is a finite abelian group, $R$ is a principal ideal domain with field of quotients an algebraic number field $K$ which splits $G$, and if $A$ is a Hopf algebra order in KG, then the Grothendieck ring of the category of finitely generated $A$-modules is isomorphic to the Grothendieck ring of the category of finitely generated RG-modules.References
- Thomas W. Hungerford, Algebra, Graduate Texts in Mathematics, vol. 73, Springer-Verlag, New York-Berlin, 1980. Reprint of the 1974 original. MR 600654
- Richard G. Larson, Group rings over Dedekind domains, J. Algebra 5 (1967), 358–361. MR 209368, DOI 10.1016/0021-8693(67)90045-2
- Richard Gustavus Larson, Hopf algebra orders determined by group valuations, J. Algebra 38 (1976), no. 2, 414–452. MR 404413, DOI 10.1016/0021-8693(76)90232-5
- Jean-Pierre Serre, Groupes de Grothendieck des schémas en groupes réductifs déployés, Inst. Hautes Études Sci. Publ. Math. 34 (1968), 37–52 (French). MR 231831
- Richard G. Swan, The Grothendieck ring of a finite group, Topology 2 (1963), 85–110. MR 153722, DOI 10.1016/0040-9383(63)90025-9
Bibliographic Information
- © Copyright 1986 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 97 (1986), 197-200
- MSC: Primary 16A54; Secondary 16A24, 18F25, 19A31
- DOI: https://doi.org/10.1090/S0002-9939-1986-0835864-3
- MathSciNet review: 835864