On Free Sabinin Algebras

Sabinin algebras are algebraic objects that capture the local structure of analytic loops in the same way in which Lie algebras capture the local structure of Lie groups. They were introduced by Sabinin and Mibeev 13 Sabinin , L. V. , Miheev , P. O. (1987). On the infinitesimal theory of local analytic loops. Dokl. Akad. Nauk SSSR 297:801–804 (in Russian). English trans.: Soviet Math. Dokl. (1988), 36:545–548. Google Scholar]].

In 1962, Shirshov 20 Shtern , A. S. ( 1986 ). Free Lie superalgebras . Sibirsk. Mat. Z. 27 : 170 – 174 (in Russian) . Google Scholar]] suggested a scheme for choosing bases of a free Lie algebra that generalizes the Hall and Lyndon–Shirshov bases. In this article, we generalize the Shirshov scheme for the case of Sabinin algebras.