Multi-parameter Quantum Groups via Quantum Quasi-Symmetric Algebras

Abstract

It is proved that the entire multi-parameter (small-)quantum groups of symmetrizable Kac-Moody algebras can be realized as certain subquotients of the cotensor Hopf algebras. This is an axiomatic construction. Hopf 2-cocycle deformations variation for the construction machinery is described, moreover, the integrable irreducible modules can be constructed using this setting, even available for those in the fundamental alcove at root of unity case.

24 pages

References in corpus (1)

• Multi-brace cotensor Hopf algebras and quantum groups

Cited by in corpus (6)

• Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$
• Multiparameter quantum groups at roots of unity
• Double-bosonization and Majid's Conjecture, (II): cases of irregular $R$-matrices and type-crossings of $F_4$, $G_2$
• Twisted deformations vs. cocycle deformations for quantum groups
• Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$
• Multiparameter quantum groups, bosonizations and cocycle deformations