The Yoneda algebra of a K2 algebra need not be another K2 algebra

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Cassidy, T.; Phan, C.; Shelton, B.;
  • Related identifiers: doi: 10.1080/00927870902829148
  • Subject: QA | 16E65 | Mathematics - Rings and Algebras
    arxiv: Mathematics::K-Theory and Homology | Mathematics::Commutative Algebra | Mathematics::Rings and Algebras

The Yoneda algebra of a Koszul algebra or a D-Koszul algebra is Koszul. K<sub>2</sub> algebras are a natural generalization of Koszul algebras, and one would hope that the Yoneda algebra of a K<sub>2</sub> algebra would be another K<sub>2</sub> algebra. We show that thi... View more
  • References (10)

    1. Roland Berger, Koszulity for nonquadratic algebras, J. Algebra 239 (2001), no. 2, 705-734. MR MR1832913 (2002d:16034)

    2. Thomas Cassidy and Brad Shelton, Generalizing the notion of Koszul algebra, Math. Z. 260 (2008), no. 1, 93-114. MR MR2413345

    3. E. L. Green, E. N. Marcos, R. Mart´ınez-Villa, and Pu Zhang, D-Koszul algebras, J. Pure Appl. Algebra 193 (2004), no. 1-3, 141-162. MR MR2076383 (2005f:16044)

    4. Edward L. Green and Roberto Mart´ınez Villa, Koszul and Yoneda algebras, Representation theory of algebras (Cocoyoc, 1994), CMS Conf. Proc., vol. 18, Amer. Math. Soc., Providence, RI, 1996, pp. 247-297. MR MR1388055 (97c:16012)

    5. D. M. Lu, J. H. Palmieri, Q. S. Wu, and J. J. Zhang, A-infinity structure on extalgebras, pre-print, 2006.

    6. Roberto Mart´ınez-Villa, Skew group algebras and their Yoneda algebras, Math. J. Okayama Univ. 43 (2001), 1-16. MR MR1913868 (2003g:18013)

    7. Justin M. Mauger, The cohomology of certain Hopf algebras associated with p-groups, Trans. Amer. Math. Soc. 356 (2004), no. 8, 3301-3323 (electronic). MR MR2052951 (2005c:16014)

    8. Christopher Phan, Generalized Koszul properties for augmented algebras, preprint, 2008.

    9. Alexander Polishchuk and Leonid Positselski, Quadratic algebras, University Lecture Series, vol. 37, American Mathematical Society, Providence, RI, 2005. MR MR2177131

    10. Stewart B. Priddy, Koszul resolutions, Trans. Amer. Math. Soc. 152 (1970), 39-60. MR MR0265437 (42 #346)

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