Universal R-matrices for quantum groups associated to simple Lie superalgebras

DOI10.3792/pjaa.67.108zbMath0744.17022OpenAlexW2026705944WikidataQ115219936 ScholiaQ115219936MaRDI QIDQ1180773

Hiroyuki Yamane

Publication date: 27 June 1992

Published in: Proceedings of the Japan Academy. Series A (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.3792/pjaa.67.108

zbMATH Keywords

quantum groupinvolutiondefining relationstwisted productsimple Lie superalgebraHopf superalgebraHopf algebraizationuniversal \(R\)-matrices

Mathematics Subject Classification ID

Related Items (15)

A Serre type theorem for affine Lie superalgebras and their quantized enveloping superalgebras ⋮ Derivation of the action and symmetries of the \(q\)-deformed \({\mathrm{AdS}}_5\times S^5\) superstring ⋮ General eigenvalue formula for Casimir invariants of type I quantum superalgebras ⋮ A q-superdimension formula for irreps of type I quantum superalgebras ⋮ Finite-dimensional representations of the quantum superalgebra \(U_ q[gl(n/m)\) and related \(q\)-identities] ⋮ Generalized root systems and the affine Lie superalgebra \(\mathrm {G}^{(1)}(3)\) ⋮ Etingof-Kazhdan quantization of Lie superbialgebras ⋮ On the Harish-Chandra homomorphism for quantum superalgebras ⋮ Eigenvalues of Casimir invariants for type I quantum superalgebras ⋮ Jacobson generators of the quantum superalgebra Uq[sl(n+1|m) and Fock representations] ⋮ The first fundamental theorem of invariant theory for the orthosymplectic supergroup ⋮ OPERATOR FORMS OF THE CLASSICAL YANG–BAXTER EQUATION IN LIE SUPERALGEBRAS ⋮ Drinfeld constructions of the quantum affine superalgebra Uq(gl(m/n̂)) ⋮ The presentation and q deformation of special linear Lie superalgebras ⋮ Automatic construction of explicit R matrices for the one-parameter families of irreducible typical highest weight (\(\dot 0_m| \dot \alpha_n\)) representations of \(U_q[gl(m| n)\)]

Cites Work

• Unnamed Item
• q-Weyl group and a multiplicative formula for universal R-matrices
• Some applications of the quantum Weyl groups
• An analogue of P.B.W. theorem and the universal R-matrix for \(U_ h\mathfrak{sl}(N+1)\)
• Universal R-matrix of the quantum superalgebra osp(2\(| 1)\)
• Harish-Chandra isomorphisms for quantum algebras
• A q-difference analogue of \(U({\mathfrak g})\) and the Yang-Baxter equation
• A new quantum group associated with a `nonstandard' braid group representation
• Lie superalgebras

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