caa a22 4500 606161295 CHVBK 20210128100634.0 cr unu---uuuuu 210128e20150401xx s 000 0 eng 10.1007/s10468-014-9497-4 doi (NATIONALLICENCE)springer-10.1007/s10468-014-9497-4 Constructing Nearly Frobenius Algebras [Elektronische Daten] [Dalia Artenstein, Ana González, Marcelo Lanzilotta] In the first part we study nearly Frobenius algebras. The concept of nearly Frobenius algebras is a generalization of the concept of Frobenius algebras. Nearly Frobenius algebras do not have traces, nor they are self-dual. We prove that the known constructions: direct sums, tensor, quotient of nearly Frobenius algebras admit natural nearly Frobenius structures. In the second part we study algebras associated to some families of quivers and the nearly Frobenius structures that they admit. As a main theorem, we prove that an indecomposable algebra associated to a bound quiver (Q, I) with no monomial relations admits a non trivial nearly Frobenius structure if and only if the quiver Q is linearly oriented of type A n ⃗ $\overrightarrow {\mathbb {A}_{n}}$ and I = 0. We also present an algorithm that determines the number of independent nearly Frobenius structures for gentle algebras without oriented cycles. Springer Science+Business Media Dordrecht, 2014 Nearly Frobenius nationallicence Quivers nationallicence Gentle algebra nationallicence Coproduct nationallicence Bimodule morphisms nationallicence Artenstein Dalia IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut González Ana IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut Lanzilotta Marcelo IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 339-367 1386-923X 18:2<339 2015 18 10468 https://doi.org/10.1007/s10468-014-9497-4 text/html Onlinezugriff via DOI BK010053 XK010053 XK010000 Metadata rights reserved Springer special CC-BY-NC licence nationallicence 1 research-article jats NATIONALLICENCE NATIONALLICENCE NL-springer NATIONALLICENCE 856 40 https://doi.org/10.1007/s10468-014-9497-4 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Artenstein Dalia IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut NATIONALLICENCE 700 1- González Ana IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut NATIONALLICENCE 700 1- Lanzilotta Marcelo IMERL-Facultad de Ingeniería, Universidad de la República, Julio Herrera y Reissig 565, CP 11300, Montevideo, Uruguay aut NATIONALLICENCE 773 0- Algebras and Representation Theory Springer Netherlands 18/2(2015-04-01), 339-367 1386-923X 18:2<339 2015 18 10468