Squared cycles in monomial relations algebras
Brian Jue
Open Mathematics, Tome 4 (2006), p. 250-259 / Harvested from The Polish Digital Mathematics Library
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Let 𝕂 be an algebraically closed field. Consider a finite dimensional monomial relations algebra Λ=𝕂Γ𝕂ΓII of finite global dimension, where Γ is a quiver and I an admissible ideal generated by a set of paths from the path algebra 𝕂Γ . There are many modules over Λ which may be represented graphically by a tree with respect to a top element, of which the indecomposable projectives are the most natural example. These trees possess branches which correspond to right subpaths of cycles in the quiver. A pattern in the syzygies of a specific factor module of the corresponding indecomposable projective module is found, allowing us to conclude that the square of any cycle must lie in the ideal I.

Publié le : 2006-01-01
EUDML-ID : urn:eudml:doc:268956 
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Brian Jue. Squared cycles in monomial relations algebras. Open Mathematics, Tome 4 (2006) pp. 250-259. http://gdmltest.u-ga.fr/item/bwmeta1.element.doi-10_2478_s11533-006-0010-0/

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