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National Repository of Grey Literature 2 records found  Search took 0.01 seconds. 
An algorithmic approach to resolutions in representation theory
 Ivánek, Adam ; Šťovíček, Jan (advisor) ; Růžička, Pavel (referee)
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
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An algorithmic approach to resolutions in representation theory
 Ivánek, Adam ; Šťovíček, Jan (advisor) ; Růžička, Pavel (referee)
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
Detailed record

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