A method of realization of bialgebras, and Hopf algebras associated to some realizations

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dc.creatorMourre, Eric
dc.date2003-12-19
dc.date.accessioned2026-07-07T04:30:49Z
dc.date.available2026-07-07T04:30:49Z
dc.descriptionThis article introduces a method, which starting from simple and quite general mathematical data, allows to construct linear algebras of operators which are, each of them, endowed with a bialgebra structure (coproduct and counity). Moreover under some explicit and natural conditions on theses mathematical data we obtain linear algebras of operators with the following property: each of them, is either a Hopf algebra, or its bialgebra structure determines a more abstract Hopf algebra associated with it. Finally, we describe a more general abstract condition for theses bialgebras to admit a unique associated Hopf algebra. The presentation is adapted to the cases where the algebras of linear operators are not finitely generated. This article is restricted to the exposition of the method of construction and to the proofs of existence and uniqueness of the structures associated with each algebra of linear operators that are constructed. Nevertheless, it may be noticed that the ideals of relations associated with bialgebras that are obtained determine an algebraic domain which is of theoretical interest .
dc.description27 pages; French
dc.identifierhttps://arxiv.org/abs/math-ph/0312049
dc.identifierhttp://arxiv.org/abs/math-ph/0312049
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/57601
dc.subjectMathematical Physics
dc.subjectQuantum Algebra
dc.subject20G42
dc.titleA method of realization of bialgebras, and Hopf algebras associated to some realizations
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