Derived tubular strongly simply connected algebras
M. Barot 
Instituto de Matem\'aticas, UNAM, 04510 M\'exico, D.F., M\'exico 

and J. A. de la Pe\~na
Instituto de Matem\'aticas, UNAM, 04510 M\'exico, D.F., M\'exico

Proc. Amer. Math. Soc. 127 (1999), 647-655.

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 $\chi_A$.