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In this thesis we study a complex mathematical object by using a simpler one. In more detail, we give a representation of an algebra (which we always assume to be finite dimensional over an algebraically closed field and with an identity) by directed graphs or quiver. We also give a representation o...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/12096 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | In this thesis we study a complex mathematical object by using a simpler one. In more detail, we give a representation of an algebra (which we always assume to be finite dimensional over an algebraically closed field and with an identity) by directed graphs or quiver. We also give a representation of modules over that algebra by using a quiver. From a quiver Q we obtain a path algebra KQ. Conversely, if A is basic, connected and finite dimensional algebra we may obtain quiver QA. The aim of this thesis is to study the representation of hereditary algebras. The main result is if Q is a finite, connected and acyclic quiver, then the algebra A = KQ is hereditary and QA = Q. |
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