Effective Detection of Nonsplit Module Extensions

Details Effective Detection of Nonsplit Module Extensions Effective Detection of Nonsplit Module Extensions

2002-06-13

arxiv.org/abs/math/0206141v3

Mathematics

Rings and Algebras

AMS-TeX; 13 pages; no figures. Revised version. To appear in Journal of Pure and Applied Algebra

Scientific paper

Let n be a positive integer, and let R be a finitely presented (but not necessarily finite dimensional) associative algebra over a computable field. We examine algorithmic tests for deciding (1) if every n-dimensional representation of R is semisimple, and (2) if there exist nonsplit extensions of non-isomorphic irreducible R-modules whose dimensions sum to no greater than n. Our basic strategy is to reduce each of the considered representation theoretic decision problems to the problem of deciding whether a particular set of commutative polynomials has a common zero. Standard methods of computational algebraic geometry can then be applied (in principle).

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