Pseudo-Frobenius Graded Algebras with Enough Idempotents |
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Authors: | Estefanía Andreu Juan |
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Affiliation: | Departmento de Matemáticas, Universidad de Murcia, Murcia, Spain |
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Abstract: | We introduce and study the notion of pseudo-Frobenius graded algebra with enough idempotents, showing that it follows the pattern of the classical concept of pseudo-Frobenius (PF) and quasi-Frobenius (QF) ring, in particular finite dimensional self-injective algebras, as studied by Nakayama, Morita, Faith, Tachikawa, etc. We show that such an algebra is characterized by the existence of a graded Nakayama form. Moreover, we prove that the pseudo-Frobenius property is preserved and reflected by covering functors, a fact which makes the concept useful in representation theory. |
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Keywords: | Covering functor Nakayama automorphism Nakayama form Pseudo-Frobenius algebra Self-injective algebra |
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