Self-Inverse Yang–Baxter Operators from (Co)Algebra Structures

✍ Scribed by F Nichita

• Publisher: Elsevier Science
• Year: 1999
• Tongue: English
• Weight: 119 KB
• Volume: 218
• Category: Article
• ISSN: 0021-8693
• DOI: 10.1006/jabr.1999.7915

✦ Synopsis

i∈I be the dual basis in V * .

Let V e ε e be the coalgebra structure given in the previous proposition. The dual algebra has the unity ε e = e * = u e * 1 , and the multiplication is given by

e j * e r = e r e i * e r 1 e j * e r 2 = e i * e r e j * e + e i * e e j * e r = 0 M e i * ⊗ e j * e = e i * e e j * e = 0 This is the algebra V * M e * u e * . On the other hand if we start with the algebra structure V M e u e we have a dual coalgebra structure on V * as follows: ε f = f e so, ε e * = 1 ε e i * = 0 therefore, ε = ε e * e * = i e i * ⊗ e * e i = e * ⊗ e * = e * e * e j * = i e i * ⊗ e j * e i = e * ⊗ e j * + e j * ⊗ e * = e * e j *