Projective modules over Frobenius algebras and Hopf comodule algebras
Martin Lorenz, Loretta FitzGerald Tokoly
TL;DR
This paper investigates the structure of projective modules and Grothendieck groups for Frobenius algebras and Hopf Galois extensions, utilizing Higman trace and Hattori-Stallings ranks as key tools.
Contribution
It introduces new results on projective modules and Grothendieck groups specifically for Frobenius algebras and certain Hopf Galois extensions, with novel formulas and techniques.
Findings
Results on projective modules over Frobenius algebras
Formulas for Grothendieck groups K_0 and G_0
Hattori-Stallings rank product formula for Hopf Galois extensions
Abstract
This note presents some results on projective modules and the Grothendieck groups K_0 and G_0 for Frobenius algebras and for certain Hopf Galois extensions. Our principal technical tools are the Higman trace for Frobenius algebras and a product formula for Hattori-Stallings ranks of projectives over Hopf Galois extensions.
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Taxonomy
TopicsAlgebraic structures and combinatorial models · Advanced Topics in Algebra · Nonlinear Waves and Solitons