891.
Generalization of Hopf algebra
slq (2) by weakening the invertibility of the generator
K, i.e., exchanging its invertibility
KK
−1=1 to the regularity K
K=K is studied. Two weak Hopf algebras are introduced: a weak Hopf algebra
wslq (2) and a
J-weak Hopf algebra
vslq (2) which are investigated in detail. The monoids of group-like elements of
wslq (2) and
vslq (2) are regular monoids, which supports the general conjucture on the connection betweek weak Hopf algebras and regular monoids.
A quasi-braided weak Hopf algebra
Ūqw is constructed from
wslq (2). It is shown that the corresponding quasi-
R-matrix is regular R
w
wR
w=R
w.
Presented at the 10th International Colloquium on Quantum Groups: “Quantum Groups and Integrable Systems”, Prague, 21–23 June
2001
Project (No. 19971074) supported by the National Natural Science Foundation of China.
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