Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of $E_6$ and $E_7$, $E_8$

Abstract

Double-bosonization construction in Majid \cite{majid1} is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \cite{HH1, HH2} have been depicted how to grow up. This paper continues to elucidate the type-crossing and inductive constructions of exceptional quantum groups of types $E_6$ and $E_7$, $E_8$, respectively, based on the generalized double-bosonization Theorem established in \cite{HH2}. Thus the Majid's expectation for the inductive constructions of $U_q(\mathfrak{g})$'s for all finite-dimensional complex simple Lie algebras is completely achieved.

24 pages

References in corpus (4)

• Multi-brace cotensor Hopf algebras and quantum groups
• Double-bosonization and Majid's conjecture, (I): rank-induction of $ABCD$
• Multi-parameter Quantum Groups via Quantum Quasi-Symmetric Algebras
• Double-bosonization and Majid's Conjecture, (II): cases of irregular $R$-matrices and type-crossings of $F_4$, $G_2$

Cited by in corpus (1)

• Quantum (dual) Grassmann superalgebra as ${\mathcal{U}}_q(\mathfrak{gl}(m|n))$-module algebra and beyond