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Yangian of the queer Lie superalgebra

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JournalCommunications in Mathematical Physics
DatePublished - Dec 1999
Issue number1
Volume208
Number of pages29
Pages (from-to)195-223
Original languageEnglish

Abstract

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.

    Research areas

  • BAXTER EQUATION, ALGEBRAS, REPRESENTATIONS

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