TY - JOUR
T1 - Quantum SL(2,R) and its irreducible representations
AU - De Commer, Kenny
AU - Dzokou Talla, Joel Right
PY - 2022
Y1 - 2022
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))
M3 - Article
JO - Journal of Operator Theory
JF - Journal of Operator Theory
SN - 0379-4024
ER -