Turaev Group Coalgebras and Twisted Drinfeld Double

作者：Wang Shuanhong^*

来源：Indiana University Mathematics Journal, 2009, 58(3): 1395-1417.

DOI：10.1512/iumj.2009.58.3569

• Hopf algebra
• Hopf dual pairing
• Turaev group coalgebra
• Quasitriangular Turaev group coalgebra
• Twisted Drinfeld double
• Cartan data

A new method of constructing Turaev group coalgebras with quasitriangular structure is introduced. Starting from a Hopf dual pairing (A, B, sigma) with appropriate homomorphisms: phi : pi --> Aut(A) and psi : pi --> Aut(B), we construct a twisted Drinfeld double D(A, B, sigma; phi, psi) which is a Turaev S(pi)-coalgebra, where the group S(pi) is a twisted semi-direct square of pi. Moreover, when A or B is finite-dimensional, we define a non-trivial quasitriangular structure on D(A, B, sigma; phi, psi). This approach allows us to produce new examples of Turaev pi-coalgebras for many Infinite groups pi Such as GL(n) (k) and (C*)(l) with l >= 1.

• 出版日期2009
• 单位东南大学