Abstract
We factor the classical functors \({ As}\mathop {\longrightarrow }\limits ^{-} { Lie}\) and \({ Dias}\mathop {\longrightarrow }\limits ^{-}{ Leib}\) through the categories \({ Pre}\hbox {-}{} { Lie}\) and \({ Pre}\hbox {-}{} { Leib}\) of two new types of algebras. Thanks to Koszul duality for binary quadratic operads, we deduce two more categories of algebras \({ Perm}\) and \({ Ricod}\) giving rise to other factorizations. This yields a triangulation of Loday’s commutative diagram of functors on Leibniz algebras and associated operads. As an application, we define a notion of extended Leibniz algebras.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.