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The weak Hopf algebras related to generalized Kac-Moody algebra
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We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying Jm=Jm−1 for some integer m. We denote this algebra by wUqτ(G). This algebra is a weak Hopf algebra if and only if m=2. 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.
Title: The weak Hopf algebras related to generalized Kac-Moody algebra
Description:
We define a kind of quantized enveloping algebra of a generalized Kac-Moody algebra G by adding a generator J satisfying Jm=Jm−1 for some integer m.
We denote this algebra by wUqτ(G).
This algebra is a weak Hopf algebra if and only if m=2.
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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