JOURNAL ARTICLE

Anti–associative algebras.

  • Published In: Journal of Algebra & Its Applications, 2026, v. 25, n. 8. P. 1 1 of 3

  • Database: Academic Search Ultimate 2 of 3

  • Authored By: Remm, Elisabeth 3 of 3

Abstract

An anti-associative algebra is a nonassociative algebra whose multiplication satisfies the identity a (b c) + (a b) c = 0. Such algebras are nilpotent. We describe the free anti-associativealgebras with a finite number of generators. Other types of nonassociative algebras, obtained either by the polarization process such as Jacobi–Jordan algebras, or obtained by deformation quantization, are associated with this class of algebras. Following Markl-Remm's work [M. Markl and E. Remm, (Non-)Koszulness of operads for n-ary algebras, galgalim and other curiosities, J. Homotopy Relat. Struct.10 (2015) 939–969], we describe the operads associated with these algebra classes and in particular the cohomology complexes related to deformations. [ABSTRACT FROM AUTHOR]

Additional Information

  • Source:Journal of Algebra & Its Applications. 2026/07, Vol. 25, Issue 8, p1
  • Document Type:Article
  • Subject Area:Science
  • Publication Date:2026
  • ISSN:0219-4988
  • DOI:10.1142/S0219498826500805
  • Accession Number:193121404
  • Copyright Statement:Copyright of Journal of Algebra & Its Applications is the property of World Scientific Publishing Company and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)

Looking to go deeper into this topic? Look for more articles on EBSCOhost.