Quantized enveloping algebras for Borcherds superalgebras

DOI10.1090/S0002-9947-98-02058-3zbMath0913.17008OpenAlexW1512729409MaRDI QIDQ4211102

Seok-Jin Kang, Georgia M. Benkart, Duncan J. Melville

Publication date: 10 September 1998

Published in: Transactions of the American Mathematical Society (Search for Journal in Brave)

Full work available at URL: https://doi.org/10.1090/s0002-9947-98-02058-3

zbMATH Keywords

quantum groupsVerma modulesLie algebrasHopf algebraquantum deformationsBorcherds superalgebraquantum Verma modulesquantum irreducible highest weight module

Mathematics Subject Classification ID

Quantum groups (quantized enveloping algebras) and related deformations (17B37) Kac-Moody (super)algebras; extended affine Lie algebras; toroidal Lie algebras (17B67)

Related Items (25)

Canonical bases for quantum generalized Kac-Moody algebras. ⋮ The extension of a quantized Borcherds superalgebra by a Hopf algebra ⋮ Generalized Kac-Moody algebras and some related topics ⋮ Weak quantum Borcherds superalgebras and their representations ⋮ Representations of spin quiver Hecke algebras for orthosymplectic Lie superalgebras ⋮ Quantum supergroups. V: Braid group action ⋮ Quantum supergroups II. Canonical basis ⋮ Quantizations of Kac-Moody algebras. ⋮ Graded dimensions and monomial bases for the cyclotomic quiver Hecke superalgebras ⋮ Quantum supergroups. I: Foundations ⋮ PBW-bases of coideal subalgebras and a freeness theorem ⋮ A fundamental representation of quantum generalized Kac-Moody algebras with one imaginary simple root ⋮ Graded Cartan determinants of the symmetric groups ⋮ Weak Hopf algebras corresponding to Borcherds-Cartan matrices. ⋮ Nichols algebras over weak Hopf algebras ⋮ Lusztig isomorphisms for Drinfel'd doubles of bosonizations of Nichols algebras of diagonal type ⋮ Some graded bialgebras related to Borcherds superalgebras ⋮ Crystal bases for Kac-Moody superalgebras ⋮ Quantum supergroups. VI: Roots of 1 ⋮ Highest weight modules over quantum queer superalgebra \(U_q(\mathfrak {q}(n))\) ⋮ Verma-type modules for quantum affine Lie algebras ⋮ Center and universal R-matrix for quantized Borcherds superalgebras ⋮ Weak quantum enveloping algebras of Borcherds superalgebras ⋮ Integrable Representations of Quantum Borcherds Superalgebras ⋮ Categorification of quantum Kac-Moody superalgebras

Cites Work

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