1. A combinatorial discussion on finite edimensional Leavitt path algebras
- Author
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Koç, Ayten, Esin, Songül, Güloğlu, Ismail, Kanuni, Müge, Koc, Ayten, Esin, Songul, Guloglu, Ismail, Kanuni, Muge, Doğuş Üniversitesi, Fen Edebiyat Fakültesi, Matematik Bölümü, TR112205, TR143120, TR6591, TR145213, Güloğlu, İsmail Ş., Fen Edebiyat Fakültesi / Faculty of Letters and Sciences Matematik - Bilgisayar / Mathematics and Computer Science, Esin, Songül, and Güloğlu, İsmail Şuayip
- Subjects
Truncated trees ,Pure mathematics ,Leavitt path algebra ,law.invention ,Leavitt Path Algebra ,Finite dimensional semisimple algebra,Leavitt path algebra,Truncated trees,Line graphs ,law ,Line graph ,FOS: Mathematics ,Finite Dimensional Semisimple Algebra ,Algebraic number ,Invariant (mathematics) ,Mathematics ,Discrete mathematics ,Finite dimensional semisimple algebra ,Semisimple algebra ,Direct sum ,Mathematics::Rings and Algebras ,General Medicine ,Mathematics - Rings and Algebras ,Truncated Trees ,Rings and Algebras (math.RA) ,Line Graphs ,Algebra representation ,Division algebra ,Isomorphism ,Line graphs - Abstract
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. In this paper we will consider the special case where all division rings are exactly the field K. All such finite dimensional semisimple algebras arise as a finite dimensional Leavitt path algebra. For this specific finite dimensional semisimple algebra A over a field K, we define a uniquely detemined specific graph - which we name as 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 {\kappa}(A)=n. 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 determine the number of distinct Leavitt path algebras of a line graph with a given number of vertices., Comment: 10 pages, 5 figures
- Published
- 2014