Research output: Contribution to journal › Article

Journal | Communications in Mathematical Physics |
---|---|

Date | Published - Dec 1999 |

Issue number | 1 |

Volume | 208 |

Number of pages | 29 |

Pages (from-to) | 195-223 |

Original language | English |

Consider the complex matrix Lie superalgebra glNjN with the standard generators

Eij , where i; j D 1; : : : ;N. Define an involutory automorphism of glNjN

by .Eij / D E-i;-j . The twisted polynomial current Lie superalgebra

g D fX.u/ 2 glNjN

TuU V .X.u// D X.-u/g

has a natural Lie co-superalgebra structure.We quantise the universal enveloping algebra U(.g/) as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld.We also construct a wide class of irreducible representations of the quantised algebra.

Eij , where i; j D 1; : : : ;N. Define an involutory automorphism of glNjN

by .Eij / D E-i;-j . The twisted polynomial current Lie superalgebra

g D fX.u/ 2 glNjN

TuU V .X.u// D X.-u/g

has a natural Lie co-superalgebra structure.We quantise the universal enveloping algebra U(.g/) as a co-Poisson Hopf superalgebra. For the quantised algebra we give a description of the centre, and construct the double in the sense of Drinfeld.We also construct a wide class of irreducible representations of the quantised algebra.

- BAXTER EQUATION, ALGEBRAS, REPRESENTATIONS

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