Results 11 to 20 of about 249,196 (276)
On the correspondence between path algebras and generalized path algebras [PDF]
Communications in Algebra, 2021 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 ...
Viktor Chust, Flávio U. Coelho
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Interpretability and Representability of Commutative Algebra, Algebraic Topology, and Topological Spectral Theory for Real-World Data. [PDF]
Adv Intell DiscovThis article investigates how persistent homology, persistent Laplacians, and persistent commutative algebra reveal complementary geometric, topological, and algebraic invariants or signatures of real‐world data. By analyzing shapes, synthetic complexes, fullerenes, and biomolecules, the article shows how these mathematical frameworks enhance ...
Ren Y, Wei GW.
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Representations of Leavitt path algebras [PDF]
Journal of Pure and Applied Algebra, 2020 We study representations of a Leavitt path algebra $L$ of a finitely separated digraph $Γ$ over a field. We show that the category of $L$-modules is equivalent to a full subcategory of quiver representations. When $Γ$ is a (non-separated) row-finite digraph we determine all possible finite dimensional quotients of $L$ after giving a necessary and ...
Koc, Ayten, Ozaydin, Murad
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Centers of Path Algebras, Cohn and Leavitt Path Algebras [PDF]
Bulletin of the Malaysian Mathematical Sciences Society, 2015 We study the center of several types of path algebras. We start with the path algebra $KE$ and prove that if the number of vertices is infinite then the center is zero. Otherwise, it coincides with the field $K$ except when the graph $E$ is a cycle in which case the center is $K[x]$, the polynomial algebra in one indeterminate.
Corrales~García, María G. +4 more
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On the dimensions of path algebras [PDF]
Mathematical Research Letters, 2014 In this paper we study the representation dimension as well as the derived dimension of the path algebra of an artin algebra over a finite and acyclic quiver.
Asadollahi, Javad, Hafezi, Rasool
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Leavitt path algebras are Bézout [PDF]
Israel Journal of Mathematics, 2018 Let $E$ be a directed graph, $K$ any field, and let $L_K(E)$ denote the Leavitt path algebra of $E$ with coefficients in $K$. We show that $L_K(E)$ is a Bézout ring, i.e., that every finitely generated one-sided ideal of $L_K(E)$ is principal.
Abrams, Gene +2 more
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Noetherian Leavitt Path Algebras and Their Regular Algebras [PDF]
Mediterranean Journal of Mathematics, 2013 In the past, it has been shown that the Leavitt path algebra $L(E)=L_K(E)$ of a graph $E$ over a field $K$ is left and right noetherian if and only if the graph $E$ is finite and no cycle of $E$ has an exit. If $Q(E)=Q_K(E)$ denotes the regular algebra over $L(E),$ we prove that these conditions are further equivalent with any of the following: $L(E ...
Aranda Pino, Gonzalo, Vaš, Lia
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Independent Rainbow Domination Numbers of Generalized Petersen Graphs P(n,2) and P(n,3)
Mathematics, 2020 We obtain new results on independent 2- and 3-rainbow domination numbers of generalized Petersen graphs P ( n , k ) for certain values of n , k ∈ N . By suitably adjusting and applying a well established technique of tropical algebra (path
Boštjan Gabrovšek +2 more
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A Combinatorial Discussion on Finite Dimensional Leavitt Path Algebras [PDF]
, 2012 Any finite dimensional semisimple algebra A over a field K is isomorphic to a direct sum of finite dimensional full matrix rings over suitable division rings.
Esin, Songul +7 more
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Braid rigidity for path algebras
Indiana University Mathematics Journal, 2022 Path algebras are a convenient way of describing decompositions of tensor powers of an object in a tensor category. If the category is braided, one obtains representations of the braid groups $B_n$ for all $n\in \N$. We say that such representations are rigid if they are determined by the path algebra and the representations of $B_2$.
Martirosyan, L., Wenzl, H.
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