Experimental Mathematics

The Alternative Operad Is Not Koszul

Askar Dzhumadil’daev and Pasha Zusmanovich

Full-text: Open access


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

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

First available in Project Euclid: 6 October 2011

Permanent link to this document

Mathematical Reviews number (MathSciNet)

Zentralblatt MATH identifier

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

Alternative operad right-alternative operad Koszulity Poincaré series


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

Export citation

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.