Product type actions of Gq

Reiji Tomatsu

doi:10.1016/j.aim.2014.09.017

Product type actions of G_q

Reiji Tomatsu^*

^*Corresponding author for this work

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

1 Citation (Scopus)

Abstract

We will study a faithful product type action of G_q, the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of G_q. This enables us to classify product type actions of SU_q(2) up to conjugacy. We also compute the intrinsic group of G_q,Ω, the 2-cocycle deformation of G_q that is naturally associated with the quantum flag manifold L^∞(T\G_q).

Original language	English
Pages (from-to)	162-196
Number of pages	35
Journal	Advances in Mathematics
Volume	269
DOIs	https://doi.org/10.1016/j.aim.2014.09.017
Publication status	Published - 2015 Jan 1
Externally published	Yes

Keywords

Depth 2 subfactors
Infinite tensor product type actions
Non-commutative Poisson boundaries
Quantum flag manifolds

ASJC Scopus subject areas

Mathematics(all)

Access to Document

10.1016/j.aim.2014.09.017

Cite this

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title = "Product type actions of Gq",

abstract = "We will study a faithful product type action of Gq, the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of Gq. This enables us to classify product type actions of SUq(2) up to conjugacy. We also compute the intrinsic group of Gq,Ω, the 2-cocycle deformation of Gq that is naturally associated with the quantum flag manifold L∞(T\Gq).",

keywords = "Depth 2 subfactors, Infinite tensor product type actions, Non-commutative Poisson boundaries, Quantum flag manifolds",

author = "Reiji Tomatsu",

note = "Funding Information: The author is grateful to Masaki Izumi for various advice. He also would like to thank Noriyuki Abe and Kenny De Commer for valuable comments on this paper. This work is supported in part by JSPS KAKENHI Grant Number 24740095 . Publisher Copyright: {\textcopyright} 2014 Elsevier Inc.",

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N1 - Funding Information: The author is grateful to Masaki Izumi for various advice. He also would like to thank Noriyuki Abe and Kenny De Commer for valuable comments on this paper. This work is supported in part by JSPS KAKENHI Grant Number 24740095 . Publisher Copyright: © 2014 Elsevier Inc.

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N2 - We will study a faithful product type action of Gq, the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of Gq. This enables us to classify product type actions of SUq(2) up to conjugacy. We also compute the intrinsic group of Gq,Ω, the 2-cocycle deformation of Gq that is naturally associated with the quantum flag manifold L∞(T\Gq).

AB - We will study a faithful product type action of Gq, the q-deformation of a connected semisimple compact Lie group G, and prove that such an action is induced from a minimal action of the maximal torus T of Gq. This enables us to classify product type actions of SUq(2) up to conjugacy. We also compute the intrinsic group of Gq,Ω, the 2-cocycle deformation of Gq that is naturally associated with the quantum flag manifold L∞(T\Gq).

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KW - Infinite tensor product type actions

KW - Non-commutative Poisson boundaries

KW - Quantum flag manifolds

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