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A combinatorial discussion on finite edimensional Leavitt path algebras
- Source :
- Volume: 43, Issue: 6 943-951, Hacettepe Journal of Mathematics and Statistics
- Publication Year :
- 2014
- Publisher :
- Hacettepe University, 2014.
-
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.<br />Comment: 10 pages, 5 figures
- 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
Subjects
Details
- Language :
- English
- ISSN :
- 2651477X
- Database :
- OpenAIRE
- Journal :
- Volume: 43, Issue: 6 943-951, Hacettepe Journal of Mathematics and Statistics
- Accession number :
- edsair.doi.dedup.....2d50d4c9a888798456a3759529a8fc92