DEGENERASI DARI VARIETY MODUL
Let r be a finite-dimensional algebra over algebraically closed field k and modrd be a collection of all d-dimensional r-module. In fact, modrd is naturally an affine variety. The general linear group GLd (k) acts on modrd and the orbits correspond to the isomorphism classes of d-dimensional r-modul...
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| Format: | Theses |
| Language: | Indonesia |
| Online Access: | https://digilib.itb.ac.id/gdl/view/15282 |
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| Institution: | Institut Teknologi Bandung |
| Language: | Indonesia |
| Summary: | Let r be a finite-dimensional algebra over algebraically closed field k and modrd be a collection of all d-dimensional r-module. In fact, modrd is naturally an affine variety. The general linear group GLd (k) acts on modrd and the orbits correspond to the isomorphism classes of d-dimensional r-modules. A module M degenerates to module N if N is contained in the closure of the orbit of M with respect to the Zariski topology. In this thesis we prove that module M in modrd degenerates to module N in modrd if and only if there is an exact sequence 0 -> Z -> Z -> M -> N -> 0 for some finite-dimensional r-module Z, and module M is semisimple if and only if the orbit of M is closed. Moreover, we define another partial orders such as virtual degeneration and hom order and prove that the degeneration, the virtual degeneration and the hom order are equivalent for algebra of finite representation type. Therefore, we obtain algebraic characterization of geometric objects. |
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