Hopf-Type Algebras |
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Authors: | Shuanhong Wang |
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Institution: | 1. Department of Mathematics , Southeast University , Nanjing, China shuanhwang2002@yahoo.com |
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Abstract: | In this article, we provide an alternative approach to the definition of a weak Hopf algebra (WHA). For an associative unital algebra A with a coassociative comultiplication Δ ∈Alg u (A, A ? A), the set of homomorphisms from A to A ? A, which do not preserve the units. If the linear maps Ξ1, Ξ2 ∈ End(A ? A), defined by Ξ1(a ? b) = Δ(a)(1 ? b), Ξ2(a ? b) = (a ? 1)Δ(b), are von Neumann regular elements in the ring End(A ? A) of endomorphisms of A ? A satisfying some appropriate assumptions, we call the A a Hopf-type algebra. We show the existence of a target, a source, a counit, and an antipode of A as in the usual WHA. |
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Keywords: | Hopf-type algebra Weak Hopf algebra |
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