We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the i...We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras （Lie di-algebras）. As another application, we prove an analogue of the Poincare-Birkhoff-Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra （CTD!-algebra）.展开更多
文摘We establish a universal approach to solutions of the word problem in the varieties of di- and tri-algebras. This approach, for example, allows us to apply Grobner-Shirshov bases method for Lie algebras to solve the ideal membership problem in free Leibniz algebras （Lie di-algebras）. As another application, we prove an analogue of the Poincare-Birkhoff-Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra （CTD!-algebra）.
