dorsal/arxiv
View SchemaHolomorphic deformation of Hopf algebras and applications to quantum groups
| Authors | Markus J. Pflaum, Martin Schottenloher |
|---|---|
| Categories | |
| ArXiv ID | q-alg/9612015 |
| URL | https://arxiv.org/abs/q-alg/9612015 |
Abstract
In this article we propose a new and so-called holomorphic deformation scheme for locally convex algebras and Hopf algebras. Essentially we regard converging power series expansion of a deformed product on a locally convex algebra, thus giving the means to actually insert complex values for the deformation parameter. Moreover we establish a topological duality theory for locally convex Hopf algebras. Examples coming from the theory of quantum groups are reconsidered within our holomorphic deformation scheme and topological duality theory. It is shown that all the standard quantum groups comprise holomorphic deformations. Furthermore we show that quantizing the function algebra of a (Poisson) Lie group and quantizing its universal enveloping algebra are topologically dual procedures indeed. Thus holomorphic deformation theory seems to be the appropriate language in which to describe quantum groups as deformed Lie groups or Lie algebras.
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"abstract": "In this article we propose a new and so-called holomorphic deformation scheme\nfor locally convex algebras and Hopf algebras. Essentially we regard converging\npower series expansion of a deformed product on a locally convex algebra, thus\ngiving the means to actually insert complex values for the deformation\nparameter. Moreover we establish a topological duality theory for locally\nconvex Hopf algebras. Examples coming from the theory of quantum groups are\nreconsidered within our holomorphic deformation scheme and topological duality\ntheory. It is shown that all the standard quantum groups comprise holomorphic\ndeformations. Furthermore we show that quantizing the function algebra of a\n(Poisson) Lie group and quantizing its universal enveloping algebra are\ntopologically dual procedures indeed. Thus holomorphic deformation theory seems\nto be the appropriate language in which to describe quantum groups as deformed\nLie groups or Lie algebras.",
"arxiv_id": "q-alg/9612015",
"authors": [
"Markus J. Pflaum",
"Martin Schottenloher"
],
"categories": [
"q-alg",
"math.QA"
],
"title": "Holomorphic deformation of Hopf algebras and applications to quantum groups",
"url": "https://arxiv.org/abs/q-alg/9612015"
},
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