Finite Gröbner-Shirshov Bases and Faithful Representations for Lee Monoids

Key Points

• To demonstrate that Lee algebras of finite rank have finite Gröbner-Shirshov bases and to construct faithful representations.
• Constructed a finite complete rewriting system for Lee monoids.
• Developed explicit constructions of faithful representations.
• Extended the representation to cases involving involution.
• Each Lee algebra of finite rank was shown to have a finite Gröbner-Shirshov basis.
• Explicit faithful representations were successfully constructed for each Lee monoid.
• The representation method was also applicable in the involution cases.