, Volume 38, Issue 2, pp 519-524

Direct Sum and Hyperbolic Complexification of Hopf Algebras

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Abstract

The problem of how to obtain a hyperboliccomplexification of a Hopf algebra from two known Hopfalgebras is discussed. We prove that this Hopf algebrais isomorphic to a direct sum of the two known Hopf algebras, and that therefore this direct sum isalso a Hopf algebra. In particular, the result can beapplied to quantum enveloping algebras.