On split twisted inner derivation triple systems with no restrictions on their 0-root spaces

The aim of this paper is to study the structure of arbitrary split twisted inner derivation triple systems. We obtain a sufficient condition for the decomposition of arbitrary twisted inner derivation triple system T {\mathscr{T}} which is of the form T = U + ∑ [ θ ] ∈ Λ T / ∼ I [ θ ] {\mathscr{T}}=U+{\sum }_{\left[\theta ]\in {\Lambda }^{{\mathscr{T}}}\text{/} \sim }{I}_{\left[\theta ]} with U U a subspace of T 0 {{\mathscr{T}}}_{0} and any I [ θ ] {I}_{\left[\theta ]} a well-described ideal of T {\mathscr{T}} , satisfying { I [ θ ] , T , I [ η ] } \left\{{I}_{\left[\theta ]},{\mathscr{T}},{I}_{\left[\eta ]}\right\} = { I [ θ ] , I [ η ] , T } \left\{{I}_{\left[\theta ]},{I}_{\left[\eta ]},{\mathscr{T}}\right\} = { T , I [ θ ] , I [ η ] } \left\{{\mathscr{T}},{I}_{\left[\theta ]},{I}_{\left[\eta ]}\right\} = { I [ θ ] , T , I [ η ] } ′ \left\{{I}_{\left[\theta ]},{\mathscr{T}},{I}_{\left[\eta ]}\right\}^{\prime} = { I [ θ ] , I [ η ] , T } ′ \left\{{I}_{\left[\theta ]},{I}_{\left[\eta ]},{\mathscr{T}}\right\}^{\prime} = { T , I [ θ ] , I [ η ] } ′ = 0 \left\{{\mathscr{T}},{I}_{\left[\theta ]},{I}_{\left[\eta ]}\right\}^{\prime} =0 if [ θ ] ≠ [ η ] \left[\theta ]\ne \left[\eta ] . In particular, a necessary and sufficient condition for the simplicity of the triple system is given.

Abstract licence: CC BY

21 more references, whose wording the paper’s licence keeps private.

A person counts once a day per paper. We keep no cookie and no address: a reader is a hash that changes every day. Any month under five reads shows no number.