Representations of the q-deformed algebra U<sub>q</sub>'(SO<sub>4</sub>)

Качурик, І. І.; Klimyk, A. U.

doi:10.1088/0305-4470/27/21/023

Cited by 6 publications

(4 citation statements)

References 9 publications

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“…Representations of the algebra so ′ q (r, 2) were studied in [19]. In fact, we generalize a part of the results of papers [18,19].…”

Section: Introductionmentioning

confidence: 71%

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Groza

2007

Preprint

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The q-deformed algebra so ′ q (r, s) is a real form of the q-deformed algebra U ′ q (so(n, C)), n = r + s, which differs from the quantum algebra U q (so(n, C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so ′ q (r, s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so ′ q (r) × so ′ q (s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All * -representations of so ′ q (r, s) are separated in the set of irreducible representations obtained in the paper.

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“…Representations of the algebra so ′ q (r, 2) were studied in [19]. In fact, we generalize a part of the results of papers [18,19].…”

Section: Introductionmentioning

confidence: 71%

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Groza

2007

Preprint

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“…24. Under the renotation of the basis elements and multiplying them by the appropriate multipliers we obtain formulas for the representation R j j Ј obtained earlier in this work.…”

Section: Irreducible Representations Of U Q ј "So 4 … Of the Clasmentioning

confidence: 81%

Representations of the q-deformed algebra Uq′(so4)

Havlíček

Klimyk

Pošta

2001

Journal of Mathematical Physics

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We study the nonstandard q-deformation U q Ј(so 4 ) of the universal enveloping algebra U͑so 4 ͒ obtained by deforming the defining relations for skew-symmetric generators of U͑so 4 ͒. This algebra is used in quantum gravity and algebraic topology.We construct a homomorphism of U q Ј(so 4 ) to the certain nontrivial extension of the Drinfeld-Jimbo quantum algebra U q (sl 2 ) 2 and show that this homomorphism is an isomorphism. By using this homomorphism we construct irreducible finitedimensional representations of the classical type and of the nonclassical type for the algebra U q Ј(so 4 ). It is proved that for q not a root of unity each irreducible finitedimensional representation of U q Ј(so 4 ) is equivalent to one of these representations. We prove that every finite-dimensional representation of U q Ј(so 4 ) for q not a root of unity is completely reducible. It is shown how to construct ͑by using the homomorphism ͒ tensor products of irreducible representations of U q Ј(so 4 ). ͓Note that no Hopf algebra structure is known for U q Ј(so 4 ).͔ These tensor products are decomposed into irreducible constituents.

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“…Representations of degenerate series of the algebra so q (r, 1) were considered in [18]. Representations of the algebra so q (r, 2) were studied in [19]. In fact, we generalize a part of the results of papers [18,19].…”

Section: Introductionmentioning

confidence: 86%

“…as well as relations (19) and (20), in which T λ (I r,r−1 ) is replaced by T λ (I r+2,r+1 ), and the relations…”

Section: Representations Of the Degenerate Principal Seriesmentioning

confidence: 99%

Degenerate Series Representations of the q-Deformed Algebra so'_q(r,s)

Groza¹

2007

SIGMA

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Abstract. The q-deformed algebra so q (r, s) is a real form of the q-deformed algebra U q (so(n, C)), n = r + s, which differs from the quantum algebra U q (so(n, C)) of Drinfeld and Jimbo. We study representations of the most degenerate series of the algebra so q (r, s). The formulas of action of operators of these representations upon the basis corresponding to restriction of representations onto the subalgebra so q (r) × so q (s) are given. Most of these representations are irreducible. Reducible representations appear under some conditions for the parameters determining the representations. All irreducible constituents which appear in reducible representations of the degenerate series are found. All * -representations of so q (r, s) are separated in the set of irreducible representations obtained in the paper.

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Representations of the q-deformed algebra U_q'(SO₄)

Cited by 6 publications

References 9 publications

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Representations of the q-deformed algebra Uq′(so4)

Degenerate Series Representations of the q-Deformed Algebra so'_q(r,s)

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Representations of the q-deformed algebra Uq'(SO4)

Cited by 6 publications

References 9 publications

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Degenerate Series Representations of the $q$-Deformed Algebra ${\rm so}'_q(r,s)$

Representations of the q-deformed algebra Uq′(so4)

Degenerate Series Representations of the q-Deformed Algebra so'q(r,s)

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Representations of the q-deformed algebra U_q'(SO₄)

Degenerate Series Representations of the q-Deformed Algebra so'_q(r,s)