an:00064656
Zbl 0760.17025
Holgate, Philip
Conditions for the linearisation of the squaring operation in genetic algebras. A review
EN
Alg??bres g??n??tiques, Cah. Math., Montpellier 38, 23-33 (1989).
1989
a
17D92 17A30 92D25
survey; genetic algebras; baric algebra; train equation; plenary powers
This is a survey of results on linearizability (in various forms) of the squaring operation in genetic algebras. It is shown that linearizability in a baric algebra is equivalent to the existence of a train equation for the plenary powers, and various classes of algebras and stronger versions of linearization are discussed. Some of the results are presented in a new manner, simplified and/or clarified.
S.Walcher (M??nchen)