<p>We give a positive answer to the following question: is it possible to define a linear operator <i>π</i><sub><i>x</i></sub> acting on the space of nonassociative polynomials linear in <i>x</i> such that the actions of <i>π</i><sub><i>x</i></sub> defined above for the associative, Lie, and Jordan cases arise as the corresponding quotient representations of this nonassociative operator <i>π</i><sub><i>x</i></sub>?</p>

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Stable Varieties of Non-Associative Algebras

  • A. V. Popov

摘要

We give a positive answer to the following question: is it possible to define a linear operator πx acting on the space of nonassociative polynomials linear in x such that the actions of πx defined above for the associative, Lie, and Jordan cases arise as the corresponding quotient representations of this nonassociative operator πx?