Quantum SL(2,R) and its irreducible representations

Kenny De Commer; Joel Right Dzokou Talla

doi:10.7900/jot.2022jun05.2380

Quantum SL(2,R) and its irreducible representations

Kenny De Commer, Joel Right Dzokou Talla

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

2 Citations (Scopus)

Abstract

We define for real q a unital ∗-algebra Uq(sl(2,R)) quantizing the universal enveloping ∗-algebra of sl(2,R). The ∗-algebra Uq(sl(2,R)) is realized as a ∗-subalgebra of the Drinfeld double of Uq(su(2)) and its dual Hopf ∗-algebra Oq(SU(2)), generated by the equatorial Podleś sphere coideal ∗-subalgebra Oq(K∖SU(2)) of Oq(SU(2)) and its associated orthogonal coideal ∗-subalgebra Uq(k)⊆Uq(su(2)). We then classify all the irreducible ∗-representations of Uq(sl(2,R))

Original language	English
Pages (from-to)	443-470
Number of pages <span style="color:red"p> <font size="1.5"> ✽ </span> </font>	28
Journal	Journal of Operator Theory
Volume	91
Issue number	2
DOIs	https://doi.org/10.7900/jot.2022jun05.2380
Publication status	Published - 2024

Keywords

quantum groups
Representation theory

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10.7900/jot.2022jun05.2380Licence: CC BY-ND

http://10.48550/arXiv.2107.04258Licence: CC BY-ND

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title = "Quantum SL(2,R) and its irreducible representations",

abstract = "We define for real q a unital ∗-algebra Uq(sl(2,R)) quantizing the universal enveloping ∗-algebra of sl(2,R). The ∗-algebra Uq(sl(2,R)) is realized as a ∗-subalgebra of the Drinfeld double of Uq(su(2)) and its dual Hopf ∗-algebra Oq(SU(2)), generated by the equatorial Podle{\'s} sphere coideal ∗-subalgebra Oq(K∖SU(2)) of Oq(SU(2)) and its associated orthogonal coideal ∗-subalgebra Uq(k)⊆Uq(su(2)). We then classify all the irreducible ∗-representations of Uq(sl(2,R))",

keywords = "quantum groups, Representation theory",

author = "{De Commer}, Kenny and {Dzokou Talla}, {Joel Right}",

year = "2024",

doi = "10.7900/jot.2022jun05.2380",

language = "English",

volume = "91",

pages = "443--470",

journal = "Journal of Operator Theory",

issn = "0379-4024",

publisher = "Theta Foundation",

number = "2",

}

TY - JOUR

T1 - Quantum SL(2,R) and its irreducible representations

AU - De Commer, Kenny

AU - Dzokou Talla, Joel Right

PY - 2024

Y1 - 2024

N2 - We define for real q a unital ∗-algebra Uq(sl(2,R)) quantizing the universal enveloping ∗-algebra of sl(2,R). The ∗-algebra Uq(sl(2,R)) is realized as a ∗-subalgebra of the Drinfeld double of Uq(su(2)) and its dual Hopf ∗-algebra Oq(SU(2)), generated by the equatorial Podleś sphere coideal ∗-subalgebra Oq(K∖SU(2)) of Oq(SU(2)) and its associated orthogonal coideal ∗-subalgebra Uq(k)⊆Uq(su(2)). We then classify all the irreducible ∗-representations of Uq(sl(2,R))

AB - We define for real q a unital ∗-algebra Uq(sl(2,R)) quantizing the universal enveloping ∗-algebra of sl(2,R). The ∗-algebra Uq(sl(2,R)) is realized as a ∗-subalgebra of the Drinfeld double of Uq(su(2)) and its dual Hopf ∗-algebra Oq(SU(2)), generated by the equatorial Podleś sphere coideal ∗-subalgebra Oq(K∖SU(2)) of Oq(SU(2)) and its associated orthogonal coideal ∗-subalgebra Uq(k)⊆Uq(su(2)). We then classify all the irreducible ∗-representations of Uq(sl(2,R))

KW - quantum groups

KW - Representation theory

UR - http://dx.doi.org/10.7900/jot.2022jun05.2380

UR - http://www.scopus.com/inward/record.url?scp=85191760856&partnerID=8YFLogxK

U2 - 10.7900/jot.2022jun05.2380

DO - 10.7900/jot.2022jun05.2380

M3 - Article

VL - 91

SP - 443

EP - 470

JO - Journal of Operator Theory

JF - Journal of Operator Theory

SN - 0379-4024

IS - 2

ER -

Quantum SL(2,R) and its irreducible representations

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FWOAL900: Quantum symmetric spaces, operator algebras and quantum cluster algebras

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Quantum SL(2,R) and its irreducible representations

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FWOAL900: Quantum symmetric spaces, operator algebras and quantum cluster algebras

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