## Centralizer construction of the Yangian of the queer Lie superalgebra

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

### Standard

Centralizer construction of the Yangian of the queer Lie superalgebra. / Nazarov, Maxim; Sergeev, Alexander.

Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday: Progress in Mathematics. Vol. 243 Part II. ed. 2006. p. 417-441.

Research output: Chapter in Book/Report/Conference proceedingOther chapter contribution

### Harvard

Nazarov, M & Sergeev, A 2006, Centralizer construction of the Yangian of the queer Lie superalgebra. in Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday: Progress in Mathematics. Part II edn, vol. 243, pp. 417-441. https://doi.org/10.1007/0-8176-4478-4_17

### APA

Nazarov, M., & Sergeev, A. (2006). Centralizer construction of the Yangian of the queer Lie superalgebra. In Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday: Progress in Mathematics (Part II ed., Vol. 243, pp. 417-441) https://doi.org/10.1007/0-8176-4478-4_17

### Vancouver

Nazarov M, Sergeev A. Centralizer construction of the Yangian of the queer Lie superalgebra. In Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday: Progress in Mathematics. Part II ed. Vol. 243. 2006. p. 417-441 https://doi.org/10.1007/0-8176-4478-4_17

### Author

Nazarov, Maxim ; Sergeev, Alexander. / Centralizer construction of the Yangian of the queer Lie superalgebra. Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday: Progress in Mathematics. Vol. 243 Part II. ed. 2006. pp. 417-441

@inbook{2816ab97798d4621a322c2401efa9eb0,
title = "Centralizer construction of the Yangian of the queer Lie superalgebra",
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. ",
keywords = "Algebra",
author = "Maxim Nazarov and Alexander Sergeev",
year = "2006",
doi = "10.1007/0-8176-4478-4_17",
language = "English",
isbn = "978-0-8176-4342-3",
volume = "243",
pages = "417--441",
booktitle = "Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday",
edition = "Part II",

}

TY - CHAP

T1 - Centralizer construction of the Yangian of the queer Lie superalgebra

AU - Nazarov, Maxim

AU - Sergeev, Alexander

PY - 2006

Y1 - 2006

N2 - 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.

AB - 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.

KW - Algebra

U2 - 10.1007/0-8176-4478-4_17

DO - 10.1007/0-8176-4478-4_17

M3 - Other chapter contribution

SN - 978-0-8176-4342-3

VL - 243

SP - 417

EP - 441

BT - Studies in Lie Theory: Dedicated to A. Joseph on his Sixtieth Birthday

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