Experimental Mathematics

The Alternative Operad Is Not Koszul

Askar Dzhumadil’daev and Pasha Zusmanovich

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Abstract

In the online compendium, J. L. Loday, Encyclopedia of Types of Algebras, it is asked whether the alternative operad is Koszul. The purpose of this note is to demonstrate that the answer to this question is negative. In doing so, we have been aided by the programs Albert and PARI/GP.

Article information

Source
Experiment. Math., Volume 20, Issue 2 (2011), 138-144.

Dates
First available in Project Euclid: 6 October 2011

Permanent link to this document
https://projecteuclid.org/euclid.em/1317924405

Mathematical Reviews number (MathSciNet)
MR2821385

Zentralblatt MATH identifier
1351.17034

Subjects
Primary: 17D05: Alternative rings
Secondary: 05A05: Permutations, words, matrices 16N40: Nil and nilpotent radicals, sets, ideals, rings 16S37: Quadratic and Koszul algebras 17-04: Explicit machine computation and programs (not the theory of computation or programming) 17DI5 18D50: Operads [See also 55P48] 65F99: None of the above, but in this section

Keywords
Alternative operad right-alternative operad Koszulity Poincaré series

Citation

Dzhumadil’daev, Askar; Zusmanovich, Pasha. The Alternative Operad Is Not Koszul. Experiment. Math. 20 (2011), no. 2, 138--144. https://projecteuclid.org/euclid.em/1317924405


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See also

  • See: Askar Dzhumadil’daev, Pasha Zusmanovich. Corrigendum to: "The Alternative Operad Is Not Koszul" by Askar Dzhumadil’daev and Pasha Zusmanovich. Experiment. Math. Volume 21, Issue 4 (2012), 418.