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A simple symmetry generating operads related to rooted planar $m$ -ary trees and polygonal numbers.

Leroux, Philippe (2007)

Journal of Integer Sequences [electronic only]

Basis for identities of the algebra of simplified insertion.

Sverchkov, S.R. (2009)

Sibirskij Matematicheskij Zhurnal

Coherent unit actions on regular operads and Hopf algebras.

Ebrahimi-Fard, Kurusch, Guo, Li (2007)

Theory and Applications of Categories [electronic only]

Lie commutators in a free diassociative algebra

A.S. Dzhumadil'daev, N.A. Ismailov, A.T. Orazgaliyev (2020)

Communications in Mathematics

We give a criterion for Leibniz elements in a free diassociative algebra. In the diassociative case one can consider two versions of Lie commutators. We give criterions for elements of diassociative algebras to be Lie under these commutators. One of them corresponds to Leibniz elements. It generalizes the Dynkin-Specht-Wever criterion for Lie elements in a free associative algebra.

Représentations matricielles des séries d'arbre reconnaissables

Symeon Bozapalidis, Athanasios Alexandrakis (1989)

RAIRO - Theoretical Informatics and Applications - Informatique Théorique et Applications

Structure theory for the group algebra of the symmetric group, with applications to polynomial identities for the octonions

Murray R. Bremner, Sara Madariaga, Luiz A. Peresi (2016)

Commentationes Mathematicae Universitatis Carolinae

This is a survey paper on applications of the representation theory of the symmetric group to the theory of polynomial identities for associative and nonassociative algebras. In §1, we present a detailed review (with complete proofs) of the classical structure theory of the group algebra $𝔽 S_{n}$ of the symmetric group $S_{n}$ over a field $𝔽$ of characteristic 0 (or $p > n$ ). The goal is to obtain a constructive version of the isomorphism $ψ : ⨁_{λ} M_{d_{λ}} (𝔽) ⟶ 𝔽 S_{n}$ where $λ$ is a partition of $n$ and $d_{λ}$ counts the standard tableaux of shape $λ$ ....

Sur la catégorie de Lusternik-Schnirelmann des algèbres de cochaînes

Bitjong Ndombol (1991)

Annales de l'institut Fourier

Nous introduisons une nouvelle définition d’un invariant bi $M$ cat pour une algèbre de cochaînes $A$ connexe et 1-connexe, de type fini sur un corps $k$ de caractéristique quelconque, et nous montrons d’une part, qu’il coïncide avec l’invariant $𝒜$ cat introduit par S. Halperin et J.-M. Lemaire et d’autre part, qu’il est invariant par extension de corps et qu’il vérifie la conjecture de Ganéa.