On the correspondence between path algebras and generalized path algebras

V Chust, FU Coelho - Communications in Algebra, 2022 - Taylor & Francis
V Chust, FU Coelho
Communications in Algebra, 2022Taylor & Francis
The concept of generalized path algebras was introduced in Coelho and Liu (2000). It was
shown in Ibáñez Cobos et al.(2008) how to obtain the Gabriel quiver of a given generalized
path algebra. In this article, we generalize the concept of generalized path algebra to allow
them to have relations, and we extend the result in Ibáñez Cobos et al.(2008) to this new
setting. Moreover, we use the extended result mentioned above to address the inverse
problem: that is, the problem of determining when a given algebra is isomorphic to a …
Abstract
The concept of generalized path algebras was introduced in Coelho and Liu (2000). It was shown in Ibáñez Cobos et al. (2008) how to obtain the Gabriel quiver of a given generalized path algebra. In this article, we generalize the concept of generalized path algebra to allow them to have relations, and we extend the result in Ibáñez Cobos et al. (2008) to this new setting. Moreover, we use the extended result mentioned above to address the inverse problem: that is, the problem of determining when a given algebra is isomorphic to a generalized path algebra in a non-trivial way.
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