The two parameter quantum groups‎ ‎$U_{r,s}(mathfrak{g})$ associated to generalized Kac-Moody algebra‎ ‎and their equitable presentation

نویسندگان

  • H. Li Zhejiang International Studies University, China
  • Q. Sun Zhejiang University of Science and Technology, China
چکیده مقاله:

We construct a family of two parameter quantum grou-\ps‎ ‎$U_{r,s}(mathfrak{g})$ associated with a generalized Kac-Moody‎ ‎algebra corresponding to symmetrizable admissible Borcherds Cartan‎ ‎matrix‎. ‎We also construct the $textbf{A}$-form $U_{textbf{A}}$ and‎ ‎the classical limit of $U_{r,s}(mathfrak{g})$‎. ‎Furthermore‎, ‎we‎ ‎display the equitable presentation for a subalgebra‎ ‎$U_{r,s}^{b-}(mathfrak{g} )$ of $U_{r,s}(mathfrak{g})$ and show‎ ‎that this presentation has the attractive feature that all of its‎ ‎generators act semisimply on finite dimensional irreducible‎ ‎$U_{r,s}(mathfrak{g})$-modules associated with the Kac-Moody algebra‎.

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the two parameter quantum groups‎ ‎$u_{r,s}(mathfrak{g})$ associated to generalized kac-moody algebra‎ ‎and their equitable presentation

we construct a family of two parameter quantum grou-ps‎ ‎$u_{r,s}(mathfrak{g})$ associated with a generalized kac-moody‎ ‎algebra corresponding to symmetrizable admissible borcherds cartan‎ ‎matrix‎. ‎we also construct the $textbf{a}$-form $u_{textbf{a}}$ and‎ ‎the classical limit of $u_{r,s}(mathfrak{g})$‎. ‎furthermore‎, ‎we‎ ‎display the equitable presentation for a subalgebra‎ ‎$u_{r,...

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the two parameter quantum groups‎ ‎$u_{r,s}(mathfrak{g})$ associated to generalized kac-moody algebra‎ ‎and their equitable presentation

we construct a family of two parameter quantum grou-ps‎ ‎$u_{r,s}(mathfrak{g})$ associated with a generalized kac-moody‎ ‎algebra corresponding to symmetrizable admissible borcherds cartan‎ ‎matrix‎. ‎we also construct the $textbf{a}$-form $u_{textbf{a}}$ and‎ ‎the classical limit of $u_{r,s}(mathfrak{g})$‎. ‎furthermore‎, ‎we‎ ‎display the equitable presentation for a subalgebra‎ ‎$u_{r,s}^{b-...

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عنوان ژورنال

دوره 39  شماره 1

صفحات  125- 149

تاریخ انتشار 2013-03-01

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