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On the Center of Quantized Enveloping Algebras

โœ Scribed by Pierre Baumann

Publisher
Elsevier Science
Year
1998
Tongue
English
Weight
266 KB
Volume
203
Category
Article
ISSN
0021-8693

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โœฆ Synopsis

Let U be a quasitriangular Hopf algebra. One may use the R-matrix of U in order to construct scalar invariants of knots. Analogously, Reshetikhin wrote down tangle invariants which take their values in the center of U. Reshetikhin's expressions thus define central elements in U. We prove here an identity characterizing some of these elements, when U is a quantized enveloping algebra. As an application, we give a proof for a statement of Faddeev, Reshetikhin, and Takhtadzhyan concerning the center of a quantized enveloping algebra.

แฎŠ 1998 Academic Press q and the quantum traces in U แ’„-modules: it is thus valid for the so-called q w x ''ribbon Hopf algebras.'' For these algebras, Reshetikhin 12 explained how invariants of certain tangles give rise to central elements. In this article, we give a formula connecting, in the case of U แ’„, some of these q elements to the previous descriptions. 244

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