Representations of the q-deformed algebra Uq'(SO4)
نویسندگان
چکیده
منابع مشابه
1 REPRESENTATIONS OF THE q-DEFORMED ALGEBRA U ′ q (so4)
We study the nonstandard q-deformation U ′ q (so 4) of the universal enveloping algebra U (so 4) obtained by deforming the defining relations for skew-symmetric generators of U (so 4). This algebra is used in quantum gravity and algebraic topology. We construct a homomor-phism φ of U ′ q (so 4) to the certain nontrivial extension of the Drinfeld–Jimbo quantum algebra U q (sl 2) ⊗2 and show that...
متن کامل1 REPRESENTATIONS OF THE q-DEFORMED ALGEBRA Uq(isoq(2))
An algebra homomorphism ψ from the q-deformed algebra U q (iso 2) with generating elements I, T 1 , T 2 and defining relations [I, T 2 ] q = T 1 , [T 1 , I] q = T 2 , [T 2 , T 1 ] q = 0 (where [A, B] q = q 1/2 AB − q −1/2 BA) to the extensionˆU q (m 2) of the Hopf algebra U q (m 2) is constructed. The algebra U q (iso 2) at q = 1 leads to the Lie algebra iso 2 ∼ m 2 of the group ISO(2) of motio...
متن کاملCLASSIFICATION THEOREM ON IRREDUCIBLE REPRESENTATIONS OF THE q-DEFORMED ALGEBRA
The aim of this paper is to give a complete classification of irreducible finite-dimensional representations of the nonstandard q-deformation U ′ q(son) (which does not coincide with the Drinfel’d-Jimbo quantum algebra Uq(son)) of the universal enveloping algebra U(son(C)) of the Lie algebra son(C) when q is not a root of unity. These representations are exhausted by irreducible representations...
متن کاملIRREDUCIBLE REPRESENTATIONS OF DEFORMED OSCILLATOR ALGEBRA AND q-SPECIAL FUNCTIONS
Different generators of a deformed oscillator algebra give rise to oneparameter families of q-exponential functions and q-Hermite polynomials related by generating functions. Connections of the Stieltjes and Hamburger classical moment problems with the corresponding resolution of unity for the q-coherent states and with ’coordinate’ operators Jacobi matrices, are also pointed out. Permanent add...
متن کاملITP-97-9E q-alg/9709035 REPRESENTATIONS OF THE q-DEFORMED ALGEBRA U ′ q(so2,2)
The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible *-representations of the q-deformed algebra U ′ q (so 2,2) which is a real form of the non-standard deformation U ′ q (so 4) of the universal enveloping algebra U (so(4, C)). These representations are described by two complex parameters and are obtained by " analytical continuati...
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ژورنال
عنوان ژورنال: Journal of Physics A: Mathematical and General
سال: 1994
ISSN: 0305-4470,1361-6447
DOI: 10.1088/0305-4470/27/21/023