On the correspondence between path algebras and generalized path algebras
نویسندگان
چکیده
The concept of generalized path algebras was introduced in Coelho and Liu (2000). It shown Ibáñez Cobos et al. (2008) how to obtain the Gabriel quiver a given algebra. In this article, we generalize algebra allow them have relations, extend result new setting. Moreover, use extended mentioned above address inverse problem: that is, problem determining when is isomorphic non-trivial way.
منابع مشابه
Generalized Path Algebras and Pointed Hopf Algebras
Most of pointed Hopf algebras of dimension p with large coradical are shown to be generalized path algebras. By the theory of generalized path algebras it is obtained that the representations, homological dimensions and radicals of these Hopf algebras. The relations between the radicals of path algebras and connectivity of directed graphs are given. 2000 Mathematics subject Classification: 16w3...
متن کاملStructures and Representations of Generalized Path Algebras
It is shown that an algebra Λ can be lifted with nilpotent Jacobson radical r = r(Λ) and has a generalized matrix unit {eii}I with each ēii in the center of Λ̄ = Λ/r iff Λ is isomorphic to a generalized path algebra with weak relations. Representations of the generalized path algebras are given. As a corollary, Λ is a finite algebra with non-zero unity element over perfect field k (e.g. a field ...
متن کاملPath Hopf Algebras and Co-path Hopf Algebras
The main goal is to study the Hopf algebra structure on quivers. The main result obtained by C. Cibils and M. Rosso is improved. That is, in the case of infinite dimensional isotypic components it is shown that the path coalgebra kQ admits a graded Hopf algebra structure if and only if Q is a Hopf quiver. All nonisomorphic point path Hopf algebras and point co-path Hopf algebras are found. The ...
متن کاملAlgebras of Quotients of Path Algebras
Leavitt path algebras are shown to be algebras of right quotients of their corresponding path algebras. Using this fact we obtain maximal algebras of right quotients from those (Leavitt) path algebras whose associated graph satisfies that every vertex connects to a line point (equivalently, the Leavitt path algebra has essential socle). We also introduce and characterize the algebraic counterpa...
متن کاملAlgebras of Quotients of Leavitt Path Algebras
We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Communications in Algebra
سال: 2021
ISSN: ['1532-4125', '0092-7872']
DOI: https://doi.org/10.1080/00927872.2021.1998516