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The Elliptic GL(n) Dynamical Quantum Group as an ?-Hopf Algebroid
Author
Source
International Journal of Mathematics and Mathematical Sciences
Issue
Vol. 2009, Issue 2009 (31 Dec. 2009), pp.1-41, 41 p.
Publisher
Hindawi Publishing Corporation
Publication Date
2009-09-07
Country of Publication
Egypt
No. of Pages
41
Main Subjects
Abstract EN
Using the language of ?-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 ??n.
We apply the generalized FRST construction and obtain an ?-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 ?-Hopf algebroid ℱell(GL(n)).
American Psychological Association (APA)
Hartwig, Jonas T.. 2009. The Elliptic GL(n) Dynamical Quantum Group as an ?-Hopf Algebroid. International Journal of Mathematics and Mathematical Sciences،Vol. 2009, no. 2009, pp.1-41.
https://search.emarefa.net/detail/BIM-480326
Modern Language Association (MLA)
Hartwig, Jonas T.. The Elliptic GL(n) Dynamical Quantum Group as an ?-Hopf Algebroid. International Journal of Mathematics and Mathematical Sciences No. 2009 (2009), pp.1-41.
https://search.emarefa.net/detail/BIM-480326
American Medical Association (AMA)
Hartwig, Jonas T.. The Elliptic GL(n) Dynamical Quantum Group as an ?-Hopf Algebroid. International Journal of Mathematics and Mathematical Sciences. 2009. Vol. 2009, no. 2009, pp.1-41.
https://search.emarefa.net/detail/BIM-480326
Data Type
Journal Articles
Language
English
Notes
Includes bibliographical references
Record ID
BIM-480326