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Proceedings of the American Mathematical Society

Published by the American Mathematical Society, the Proceedings of the American Mathematical Society (PROC) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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Derived tubular strongly simply connected algebras
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by M. Barot and J. A. de la Peña PDF
Proc. Amer. Math. Soc. 127 (1999), 647-655 Request permission

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
  • 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
  • © Copyright 1999 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 127 (1999), 647-655
  • MSC (1991): Primary 16G10, 16G60, 18E30
  • DOI: https://doi.org/10.1090/S0002-9939-99-04531-1
  • MathSciNet review: 1468181