Gr(o)bner-Shirshov Bases for Replicated Algebras

• 来源期刊: 代数集刊（英文版）
• 关键词: di-algebra tri-algebra Gr(o)bner-Shirshov basis
• 年，卷（期）: 2017,（4）
• 页码范围: 563-576
• 页数: 14页
• 语种: 英文
• DOI: 10.1142/S1005386717000372

摘要

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 Gr(o)bner 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 Poincaré-Birkhoff Witt Theorem for universal enveloping associative tri-algebra of a Lie tri-algebra (CTD1-algebra).