Dual pairs of quantum moment maps and doubles of Hopf algebras

Gus Schrader; Alexander Shapiro

doi:10.1016/j.jalgebra.2017.08.021

Dual pairs of quantum moment maps and doubles of Hopf algebras

Gus Schrader, Alexander Shapiro^*

^*Corresponding author for this work

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

Abstract

Given a dual pair of topological Hopf algebras A,A^⁎, under mild conditions there exists a natural associative algebra homomorphism D(A)→H(A) between the corresponding Drinfeld double D(A) and Heisenberg double H(A). We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck–Springer resolution arises in this context.

Original language	English (US)
Pages (from-to)	74-89
Number of pages	16
Journal	Journal of Algebra
Volume	492
DOIs	https://doi.org/10.1016/j.jalgebra.2017.08.021
State	Published - Dec 15 2017
Externally published	Yes

Keywords

Drinfeld double
Grothendieck–Springer resolution
Heisenberg double
Hopf algebras
Quantum groups
Quantum moment maps
Reflection equation algerbas

ASJC Scopus subject areas

Algebra and Number Theory

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10.1016/j.jalgebra.2017.08.021

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abstract = "Given a dual pair of topological Hopf algebras A,A⁎, under mild conditions there exists a natural associative algebra homomorphism D(A)→H(A) between the corresponding Drinfeld double D(A) and Heisenberg double H(A). We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck–Springer resolution arises in this context.",

keywords = "Drinfeld double, Grothendieck–Springer resolution, Heisenberg double, Hopf algebras, Quantum groups, Quantum moment maps, Reflection equation algerbas",

author = "Gus Schrader and Alexander Shapiro",

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AU - Schrader, Gus

AU - Shapiro, Alexander

PY - 2017/12/15

Y1 - 2017/12/15

N2 - Given a dual pair of topological Hopf algebras A,A⁎, under mild conditions there exists a natural associative algebra homomorphism D(A)→H(A) between the corresponding Drinfeld double D(A) and Heisenberg double H(A). We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck–Springer resolution arises in this context.

AB - Given a dual pair of topological Hopf algebras A,A⁎, under mild conditions there exists a natural associative algebra homomorphism D(A)→H(A) between the corresponding Drinfeld double D(A) and Heisenberg double H(A). We construct this homomorphism using a pair of commuting quantum moment maps, and then use it to provide a homomorphism of certain reflection equation algebras. We also explain how the quantization of the Grothendieck–Springer resolution arises in this context.

KW - Drinfeld double

KW - Grothendieck–Springer resolution

KW - Heisenberg double

KW - Hopf algebras

KW - Quantum groups

KW - Quantum moment maps

KW - Reflection equation algerbas

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VL - 492

SP - 74

EP - 89

JO - Journal of Algebra

JF - Journal of Algebra

ER -

Dual pairs of quantum moment maps and doubles of Hopf algebras

Abstract

Keywords

ASJC Scopus subject areas

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