ORBITS AND TEST ELEMENTS IN FREE LEIBNIZ ALGEBRAS OF RANK TWO

Ozkurt Z.

COMMUNICATIONS IN ALGEBRA, vol.43, no.8, pp.3534-3544, 2015 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 43 Issue: 8
  • Publication Date: 2015
  • Doi Number: 10.1080/00927872.2014.982806
  • Journal Name: COMMUNICATIONS IN ALGEBRA
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.3534-3544
  • Çukurova University Affiliated: Yes

Abstract

Let F be the free Leibniz algebra of rank two over a field K of characteristic zero freely generated by x(1) and x(2). In this article we show that an endomorphism of F which preserves the orbit of a nontrivial element of F is an automorphism. Using this result, we determine some test elements of F.