Yangian of the queer Lie superalgebra

Maxim Nazarov

doi:10.1007/s002200050754

Yangian of the queer Lie superalgebra

Maxim Nazarov

Mathematics

Research output: Contribution to journal › Article › peer-review

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.

Original language	English
Pages (from-to)	195-223
Number of pages	29
Journal	Communications in Mathematical Physics
Volume	208
Issue number	1
DOIs	https://doi.org/10.1007/s002200050754
Publication status	Published - Dec 1999

Keywords

BAXTER EQUATION
ALGEBRAS
REPRESENTATIONS

Access to Document

10.1007/s002200050754

http://arxiv.org/abs/math.QA/9902146

Cite this

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abstract = "Consider the complex matrix Lie superalgebra glNjN with the standard generatorsEij , where i; j D 1; : : : ;N. Define an involutory automorphism of glNjNby .Eij / D E-i;-j . The twisted polynomial current Lie superalgebrag D fX.u/ 2 glNjNTuU V .X.u// D X.-u/ghas 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.",

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AB - Consider the complex matrix Lie superalgebra glNjN with the standard generatorsEij , where i; j D 1; : : : ;N. Define an involutory automorphism of glNjNby .Eij / D E-i;-j . The twisted polynomial current Lie superalgebrag D fX.u/ 2 glNjNTuU V .X.u// D X.-u/ghas 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.

KW - BAXTER EQUATION

KW - ALGEBRAS

KW - REPRESENTATIONS

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