Person: KOÇ, AYTEN
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Publication The Module Category of Leavitt and Cohn Leavitt Path algebras(2014) KOÇ, AYTEN; 112205Publication Representations of Leavitt Path Algebras over an Additive Category with Krull-Schmidt(2016) KOÇ, AYTEN; 112205Publication Irreducible Representations of Leavitt Path Algebras of Polynomial Growth(2017) KOÇ, AYTEN; 112205Publication Gelfand-Kirillov Boyutu Sonlu Olan Leavitt Yol Cebirlerinin Yapıları ve Temsilleri(2018) KOÇ, AYTEN; 112205Publication A combinatorial discussion on finite dimensional Leavitt path algebras(Hacettepe Univ, Fac Sci, Hacettepe Univ, Fac Sci, Beytepe, Ankara 06800, Turkey, 2014) Esin, Songül; Güloğlu, İsmail; Kanuni, Müge; KOÇ, AYTEN; 112205; 145213Any 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. We shall consider the direct sum of finite dimensional full matrix rings over a field K. All such finite dimensional semisimple algebras arise as finite dimensional Leavitt path algebras. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely determined specific graph - called a truncated tree associated with A - whose Leavitt path algebra is isomorphic to A. We define an algebraic invariant kappa(A) for A and count the number of isomorphism classes of Leavitt path algebras with the same fixed value of kappa(A). Moreover, we find the maximum and the minimum K-dimensions of the Leavitt path algebras. of possible trees with a given number of vertices and we also determine the number of distinct Leavitt path algebras of line graphs with a given number of vertices.Publication Finite-dimensional representations of Leavitt path algebras(Walter De Gruyter Gmbh, Genthiner Strasse 13, D-10785 Berlin, Germany, 2018-07) Özaydın, Murad; KOÇ, AYTEN; 112205When Gamma is a row-finite digraph, we classify all finite-dimensional modules of the Leavitt path algebra L(Gamma) via an explicit Morita equivalence given by an effective combinatorial (reduction) algorithm on the digraph Gamma. The category of (unital) L(Gamma)-modules is equivalent to a full subcategory of quiver representations of Gamma. However, the category of finite-dimensional representations of L(Gamma) is tame in contrast to the finite-dimensional quiver representations of G, which are almost always wild.Publication Cemal Koc ve Matematik(2010) Esin, Songül; Güloğlu, İsmail; Kanuni, Müge; KOÇ, AYTEN; 112205; 145213Publication Representations of Leavitt and Cohn Leavitt Path algebras(2014) KOÇ, AYTEN; 112205The purpose of this talk is to present an explicit classification of all finite dimensional representations of an Leavit pathh algebra.Publication Finite Dimensional Quotients of Leavitt path Algebras of Digraphs(2013) KOÇ, AYTEN; 112205Publication Gelfrand-Kirillov Boyutu Sonlu Olan Leavitt Yol Cebirlerinin Yapısı ve Temsilleri(2018-09) KOÇ, AYTEN; 112205Leavitt yol cebirleri (kısaca LPA: Leavitt Patlı Algebra) 2004 yılında Ara- Moreno-Pardo ve Abrams-Arando Pino tarafından, çizge C'*-cebirlerinin (80’lerde tanımlanan) cebirsel benzerleri olarak tanımlandı ama kökleri Bili Leavitt’iıı 60’lardaki çalışmalarına dayanır. LPA’nın modül kategorisinin çizgenin ok temsillerinin bir alt kategorisine denk olmasından başlayarak temsil sınıflandırmaları yapılabilir.Konuşmanın ilk kısmında gerekli temel tanımlar verilecek ve de LPA’nın cebirsel özellikleri ile çizgenin geometrisi arasındaki ilişki vurgulanacaktır, ikinci kısımda ise (M. Özaydın ile ortak çalışma) Gelfand-Kirillov boyutu sonlu olan Leavitt yol cebirlerinin yapıları ve temsillerinden bahsedilecektir.