In this thesis we describe an algorithm and implement a construction of a projective resolution and minimal projective resolution in the representation the- ory of finite-dimensional algebras. In this thesis finite-dimensional algebras are KQ /I where KQ is a path algebra and I is an admissible ideal. To implement the algorithm we use the package QPA [9] for GAP [2]. We use the theory of Gröbners basis of KQ-modules and the theory described in article Minimal Pro- jective Resolutions written by Green, Solberg a Zacharia [5]. First step is find a direct sum such that i∈Tn fn∗ i KQ = i∈Tn−1 fn−1 i KQ ∩ i∈Tn−2 fn−2 i I. Next important step to construct the minimal projective resolution is separate nontri- vial K-linear combinations in i∈Tn−1 fn−1 i I + i∈Tn fn i J from fn∗ i . The Modules of the minimal projective elements are i∈Tn (fn i KQ)/(fn i I). 1
| Identifer | oai:union.ndltd.org:nusl.cz/oai:invenio.nusl.cz:346726 |
| Date | January 2016 |
| Creators | Ivánek, Adam |
| Contributors | Šťovíček, Jan, Růžička, Pavel |
| Source Sets | Czech ETDs |
| Language | Slovak |
| Detected Language | English |
| Type | info:eu-repo/semantics/masterThesis |
| Rights | info:eu-repo/semantics/restrictedAccess |
Page generated in 0.0024 seconds