Derived tubular strongly simply connected algebras

Let A be a finite dimensional algebra over an algebraically closed field k. Assume A=kQ/I for a connected quiver Q and an admissible ideal I of kQ. We study algebras A which are derived equivalent to tubular algebras. If A is strongly simply connected and Q has more than six vertices, then A is deri...

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Bibliographic Details
Published in:Proceedings of the American Mathematical Society 1999-03, Vol.127 (3), p.647-655
Main Authors: Barot, M., de la Peña, J. A.
Format: Article
Language:English
Subjects:
Algebra
Mathematical theorems
Mathematical vectors
Morphisms
Polynomials
Spectral index
Spectral reflectance
Vertices
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Summary:Let A be a finite dimensional algebra over an algebraically closed field k. Assume A=kQ/I for a connected quiver Q and an admissible ideal I of kQ. We study algebras A which are derived equivalent to tubular algebras. If A is strongly simply connected and Q has more than six vertices, then A is derived tubular if and only if (i) the homological quadratic form \chi_A is a non-negative of corank two and (ii) no vector of \chi_A ^{-1}(1) is orthogonal (with respect tho the homological bilinear form) to the radical of \chi_A.
ISSN:0002-9939
1088-6826
DOI:10.1090/S0002-9939-99-04531-1