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| Ribbon Hopf Superalgebras and Drinfel'd Double |
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Citation： |
Jialei CHEN,Shilin YANG.Ribbon Hopf Superalgebras and Drinfel'd Double[J].Chinese Annals of Mathematics B,2018,39(6):1047~1064 |
| Page view： 676
Net amount： 514 |
Authors： |
Jialei CHEN; Shilin YANG |
Foundation： |
This work was supported by the National Natural Science
Foundation of China (Nos.11701019, 11671024) and the Natural
Science Foundation of Beijing (No.1162002). |
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| Abstract： |
Finite dimensional ribbon Hopf (super) algebras play an important
role in constructing invariants of 3-manifolds. In the present
paper, the authors give a necessary and sufficient condition for the
Drinfel'd double of a finite dimensional Hopf superalgebra to have a
ribbon element. The criterion can be seen as a generalization of
Kauffman and Radford's result in the non-super situation to the
$\mathbb{Z}_{2}$-graded situation, however, the derivation of the
result in the $\mathbb{Z}_{2}$-graded case will be much more
complicated. |
Keywords： |
Hopf superalgebras, Drinfel'd double, Ribbon element |
Classification： |
16W30, 17A70, 81R50 |
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