We define a new kind quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a new generator J satisfying J m = J for some integer m. We denote this algebra by wUThis algebra is a weak Hopf algebra if and only if m = 2, 3. In general, it is a bialgebra, and contains a Hopf subalgebra. This Hopf subalgebra is isomorphic to the usually quantum envelope algebra Uq(G) of a generalized Kac-Moody algebra G.

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