An abstract approach to algebras of braids and ties

Key Points

• To unify and generalize the existing types of braid and tie algebras in literature, including new variants.
• Constructed algebras using approaches based on previous work by Marin.
• Considered existing braids and ties algebras and their properties for the construction of new ones.
• Developed a comprehensive framework for understanding various braid and tie algebras.
• Introduced new algebras alongside generalizations of established ones.