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| Titel: |
Combinatorial Algorithms for Computing Degenerations of Modules of Finite Dimension |
| Auteur: |
Mróz, Andrzej Zwara, Grzegorz |
| Verschenen in: |
Fundamenta informaticae |
| Paginering: | Jaargang 132 (2014) nr. 4 pagina's 519-532 |
| Jaar: |
2014-09-26 |
| Inhoud: |
We present combinatorial algorithms for solving three problems that appear in the study of the degeneration order ≤deg for the variety of finite-dimensional modules over a k-algebra Λ, where M ≤deg N means that a module N belongs to an orbit closure $\overline{\cal{O}(M)}$ of a module M in the variety of Λ-modules. In particular, we introduce algorithmic techniques for deciding whether or not the relation M ≤deg N holds and for determining all predecessors (resp. succesors) of a given module M with respect to ≤deg. The order ≤deg plays an important role in modern algebraic geometry and module theory. Applications of our technique and experimental tests for particular classes of algebras are presented. The results show that a computer algebra technique and algorithmic computer calculations provide important tools in solving theoretical mathematics problems of high computational complexity. The algorithms are implemented and published as a part of an open source GAP package called QPA. |
| Uitgever: |
IOS Press |
| Bronbestand: |
Elektronische Wetenschappelijke Tijdschriften |
Details van artikel 2 van 7 gevonden artikelen
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