On Free Sabinin Algebras

Abstract

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].

In 1962, Shirshov [20] 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.

Key Words:

• Hyperalgebras
• Linear basis
• Loop
• Sabinin algebra
• Shirshov scheme

ACKNOWLEDGMENTS

The author is thankful to Prof. I. P. Shestakov for suggesting this problem and valuable conversations about the results of this article.

Notes

Communicated by I. Shastakov.