The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid

The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid

Using the language of 𝔥-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, ℱell(GL(n)), from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra 𝔰&#x1...

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Main Author: Jonas T. Hartwig
Format: Article
Language:English
Published: Hindawi Limited 2009-01-01
Series:International Journal of Mathematics and Mathematical Sciences
Online Access:http://dx.doi.org/10.1155/2009/545892
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spelling doaj-472b42d54bc045738f02455de0ceb4302020-11-24T23:43:37ZengHindawi LimitedInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252009-01-01200910.1155/2009/545892545892The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf AlgebroidJonas T. Hartwig0Korteweg-de Vries Institute for Mathematics, University of Amsterdam, Postbus 94248, 1090 GE Amsterdam, The NetherlandsUsing the language of 𝔥-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, ℱell(GL(n)), from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra 𝔰𝔩n. We apply the generalized FRST construction and obtain an 𝔥-bialgebroid ℱell(M(n)). Natural analogs of the exterior algebra and their matrix elements, elliptic minors, are defined and studied. We show how to use the cobraiding to prove that the elliptic determinant is central. Localizing at this determinant and constructing an antipode we obtain the 𝔥-Hopf algebroid ℱell(GL(n)).http://dx.doi.org/10.1155/2009/545892
collection DOAJ
language English
format Article
sources DOAJ
author Jonas T. Hartwig
spellingShingle Jonas T. Hartwig
The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
International Journal of Mathematics and Mathematical Sciences
author_facet Jonas T. Hartwig
author_sort Jonas T. Hartwig
title The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
title_short The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
title_full The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
title_fullStr The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
title_full_unstemmed The Elliptic GL(n) Dynamical Quantum Group as an 𝔥-Hopf Algebroid
title_sort elliptic gl(n) dynamical quantum group as an 𝔥-hopf algebroid
publisher Hindawi Limited
series International Journal of Mathematics and Mathematical Sciences
issn 0161-1712
1687-0425
publishDate 2009-01-01
description Using the language of 𝔥-Hopf algebroids which was introduced by Etingof and Varchenko, we construct a dynamical quantum group, ℱell(GL(n)), from the elliptic solution of the quantum dynamical Yang-Baxter equation with spectral parameter associated to the Lie algebra 𝔰𝔩n. We apply the generalized FRST construction and obtain an 𝔥-bialgebroid ℱell(M(n)). Natural analogs of the exterior algebra and their matrix elements, elliptic minors, are defined and studied. We show how to use the cobraiding to prove that the elliptic determinant is central. Localizing at this determinant and constructing an antipode we obtain the 𝔥-Hopf algebroid ℱell(GL(n)).
url http://dx.doi.org/10.1155/2009/545892
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AT jonasthartwig ellipticglndynamicalquantumgroupasanx1d525hopfalgebroid
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