A diagram connecting Symmetric Leibniz algebras with Lie-admissible algebras

Abstract

In this paper we study symmetric Leibniz and related algebras, namely symmetric dialgebras and symmetric Perm-algebras. We also calculate their Koszul duals, if not known. This will give us Lie-admissible algebras and new types of algebras, which we call commutative and associative admissible algebras. Finally we prove that all operads describing the considered algebras are Koszul.

Cited by in corpus (1)

• The algebraic and geometric classification of nilpotent weakly associative and symmetric Leibniz algebras