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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Derived tubular strongly
simply connected algebras


Authors: M. Barot and J. A. de la Peña
Journal: Proc. Amer. Math. Soc. 127 (1999), 647-655
MSC (1991): Primary 16G10, 16G60, 18E30.
MathSciNet review: 1468181
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Abstract: 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 $\chi _A$.


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Additional Information

M. Barot
Affiliation: Instituto de Matemáticas, UNAM, 04510 México, D.F., México
Email: barot@gauss.matem.unam.mx

J. A. de la Peña
Affiliation: Instituto de Matemáticas, UNAM, 04510 México, D.F., México
Email: jap@penelope.matem.unam.mx

DOI: http://dx.doi.org/10.1090/S0002-9939-99-04531-1
PII: S 0002-9939(99)04531-1
Received by editor(s): December 2, 1996
Received by editor(s) in revised form: June 12, 1997
Additional Notes: This work was partially supported by CONACYT and DGAPA, UNAM
Communicated by: Ken Goodearl
Article copyright: © Copyright 1999 American Mathematical Society