Simple algebras of invariant operators (Q2762288)

Comtrans algebras were introduced as algebras with two trilinear operators, a commutator \([x,y,z]\) and a translator \(\langle x,y,z\rangle\), which satisfy certain identities. Previously known simple comtrans algebras arise from rectangular matrices, simple Lie algebras, spaces equipped with a bilinear form having trivial radical, spaces of Hermitian operators over a field with a minimum polynomial \(x^2+1\).NEWLINENEWLINENEWLINEThe paper is about generalizing the Hermitian case to the so-called invariant case. The main result of the paper shows that the vector space of \(n\)-dimensional invariant operators furnishes some comtrans algebra structures, which are simple provided that certain Jordan and Lie algebras are simple.