(Non-)Koszulness of operads for n-ary algebras, galgalim and other curiosities

Abstract

We investigate operads for various n-ary algebras. As a useful tool we introduce galgalim - analogs of the Lie-hedra for n-ary algebras. We then focus to algebras with one anti-associative operation. We describe the relevant part of the deformation cohomology for this type of algebras using the minimal model for the anti-associative operad. We also discuss free partially associative algebras and formulate some open problems.

Substantially revised and extended version

References in corpus (4)

• Koszul duality of operads and homology of partition posets
• A Poincaré-Birkhoff-Witt criterion for Koszul operads
• n-ary associative algebras, cohomology, free algebras and coalgebras
• Notes on Cohomologies of Ternary Algebras of Associative Type

Cited by in corpus (6)

• Quillen homology for operads via Gröbner bases
• Special and exceptional mock-Lie algebras
• Free resolutions via Gröbner bases
• Operads for n-ary algebras - calculations and conjectures
• A class of nonassociative algebras including flexible and alternative algebras, operads and deformations
• Universal deformation formulas