Combinatorial Algorithms for Computing Degenerations of Modules of Finite Dimension

• Autorzy: Mróz, A. , Zwara, G.
• Języki publikacji: EN

Abstrakty

EN

We present combinatorial algorithms for solving three problems that appear in the study of the degeneration order ≤_degfor the variety of finite-dimensional modules over a k-algebra Δ, where M ≤_deg N means that a module N belongs to an orbit closure O(M) of a module M in the variety of Δ-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.

Słowa kluczowe

EN

combinatorial analysis; computer algorithms; dimensions; modules; problem solving

• Czasopismo: Fundamenta Informaticae
• Rocznik: 2014
• Tom: Vol. 132, nr 4
• Strony: 519--532
• Opis fizyczny: Bibliogr. 32 poz.

Twórcy

autor

Mróz, A.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University Chopina 12/18, 87-100 Toruń, Poland,

autor

Zwara, G.

• Faculty of Mathematics and Computer Science, Nicolaus Copernicus University Chopina 12/18, 87-100 Toruń, Poland,

Bibliografia

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Identyfikatory

DOI

10.3233/FI-2014-1057