Jordan elements and Left-Center of a Free Leibniz algebra | Zendy

Askar Dzhumadil’daev | Zendy

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Jordan elements and Left-Center of a Free Leibniz algebra

Author(s) -

Askar Dzhumadil’daev

Publication year - 2011

Publication title -

electronic research announcements

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.865

H-Index - 23

ISSN - 1935-9179

DOI - 10.3934/era.2011.18.31

Subject(s) - mathematics , center (category theory) , subalgebra , jordan algebra , element (criminal law) , centralizer and normalizer , algebra over a field , extension (predicate logic) , free algebra , pure mathematics , multilinear algebra , free probability , division algebra , algebra representation , cellular algebra , computer science , programming language , chemistry , political science , law , crystallography

An element of a free Leibniz algebra is called Jordan if it belongs to a free Leibniz-Jordan subalgebra. Elements of the Jordan commutant of a free Leibniz algebra are called weak Jordan. We prove that an element of a free Leibniz algebra over a field of characteristic 0 is weak Jordan if and only if it is left-central. We show that free Leibniz algebra is an extension of a free Lie algebra by left-center. We find the dimensions of the homogeneous components of the Jordan commutant and the base of its multilinear part. We find criterion for an element of free Leibniz algebra to be Jordan.

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