Centralizer construction of the Yangian of the queer Lie superalgebra

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Publication details

Title of host publicationStudies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday
DatePublished - 2006
Pages417-441
Number of pages25
Volume243
EditionPart II
Original languageEnglish
ISBN (Electronic)978-0-8176-4478-9

Abstract

Consider the complex matrix Lie superalgebra $ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $Unknown control sequence '\mathfrak' with the standard generators E ij where i, j = ±1, . . . , ± N. Define an involutive automorphism ¿ of $ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $Unknown control sequence '\mathfrak' by ¿(E ij) = E -i,-j . The queer Lie superalgebra qN is the fixed point subalgebra in $ \mathfrak{g}\mathfrak{l}_{\left. N \right|N} $Unknown control sequence '\mathfrak' relative to ¿. Consider the twisted polynomial current Lie superalgebra
$ \mathfrak{g} = \left\{ {X\left( t \right) \in \mathfrak{g}\mathfrak{l}_{\left. N \right|N} \left[ t \right]:\eta \left( {X\left( t \right)} \right) = X\left( { - t} \right)} \right\} $Unknown control sequence '\mathfrak'
. The enveloping algebra U( $ \mathfrak{g} $Unknown control sequence '\mathfrak' ) of the Lie superalgebra g has a deformation, called the Yangian of qN. For each M = 1,2, . . . , denote by A N M the centralizer of qM ¿ q N+M in the associative superalgebra U(q N+M ). In this article we construct a sequence of surjective homomorphisms U(qN) ¿ A N 1 ¿ A N 2 ¿ . . . . We describe the inverse limit of the sequence of centralizer algebras A N 1 , A N 2 , . . . in terms of the Yangian of qN.

    Research areas

  • Algebra

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