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Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952

Proceedings of the Estonian Academy of Sciences

ISSN 1736-7530 (electronic)   ISSN 1736-6046 (print)
Formerly: Proceedings of the Estonian Academy of Sciences, series Physics & Mathematics and  Chemistry
Published since 1952
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On the non-Koszulity of ternary partially associative operad; pp. 355–363

(Full article in PDF format) doi: 10.3176/proc.2010.4.15


Authors

Elisabeth Remm

Abstract

We prove that the operad for ternary partially associative algebras is non Koszul. The aim is to underline the problem of computing the dual operad when we consider quadratic operad for n-ary algebras in particular when n is odd. In fact, the dual operad is generally defined in the graded (differential) operad framework. The result of non-Koszulity extends for other operads for (2p + 1)-ary partially associative algebras although the operads for (2p)-ary partially associative algebras are Koszul.

Keywords

n-ary algebras, operads, partial/total associativity, degree d generating operation, Koszulity.

References

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doi:10.2307/1970484

  2. Ginzburg , V. and Kapranov , M. Koszul duality for operads. Duke Math. J. , 1994 , 76 , 203–272.
doi:10.1215/S0012-7094-94-07608-4

  3. Gnedbaye , A. V. Opérades des algèbres k + 1-aires. In Operads: Proceedings of Renaissance Conferences (Hartford , CT/Luminy , 1995)} , 83–113 , Contemp. Math. , 202. Amer. Math. Soc. , Providence , RI , 1997.

  4. Gnedbaye , A. V. and Wambst , M. Jordan triples and operads. J. Algebra , 2000 , 231 , 744–757.
doi:10.1006/jabr.2000.8368

  5. Goze , M. and Remm , E. Lie-admissible algebras and operads. J. Algebra , 2004 , 273 , 129–152.
doi:10.1016/j.jalgebra.2003.10.015

  6. Goze , M. and Remm , E. Lie admissible coalgebras. J. Gen. Lie Theory Appl. , 2007 , 1 , 19–28.

  7. Goze , N. and Remm , E. n-ary associative algebras , cohomology , free algebras and coalgebras. arXiv:math/0803.0553.

  8. Markl , M. and Remm , E. (Non-)Koszulity of operads for n-ary algebras , cohomology and deformations. arXiv:math/0907.1505.

  9. Markl , M. , Shnider , S. , and Stasheff , J. Operads in Algebra , Topology and Physics. Mathematical Surveys and Monographs , 96. American Mathematical Society , Providence , RI , 2002.

10. Remm , E. and Goze , M. On the algebras obtained by tensor product. arXiv:math/0606105.
 
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Current Issue: Vol. 68, Issue 4, 2019




Publishing schedule:
No. 1: 20 March
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