Double-bosonization and Majid's Conjecture, (III): type-crossing and inductions of E₆ and E₇, E₈

2016/01/17 by Hongmei Hu, Naihong Hu, Hu, Hongmei +1 · 1 citation
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Black Holes and Theoretical Physics #FOS: Mathematics #Quantum Algebra (math.QA) #Representation Theory (math.RT)

paper · pdf · doi:10.48550/arxiv.1601.04320

openalex publication_date 2016/01/17 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Double-bosonization construction in Majid \citemajid1 is expectedly allowed to generate a tree of quantum groups. Some main branches of the tree in \citeHH1, 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 E₆ and E₇, E₈, respectively, based on the generalized double-bosonization Theorem established in \citeHH2. 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.

Citations

• Double-bosonization and Majid's Conjecture, (II): cases of irregular R-matrices and type-crossings of F₄, G₂

Cited by

• Quantum (dual) Grassmann superalgebra as \mathcal U_q(\mathfrakgl(m|n))-module algebra and beyond

Related

• Double-bosonization and Majid's Conjecture, (II): cases of irregular R-matrices and type-crossings of F₄, G₂
• Braided Geometry and the Inductive Construction of Lie Algebras and Quantum Groups
• Double-Bosonisation and the Construction of U_q(g)
• Some Comments on Bosonisation and Biproducts
• Dual braided quantum E(2) groups