On modular spaces of semisimple Drinfeld doubles

2002/04/30 by Libor Šnobl, L. Snobl · 2 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Nonlinear Waves and Solitons #hep-th

paper · pdf · doi:10.1088/1126-6708/2002/09/018

published as JHEP 0209 (2002) 018 · 15 pages; introduction enlarged, added references

openalex publication_date 2002/09/06 · arxiv created 2002/09/19 · arxiv updated 2009/11/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/29

Abstract

We construct modular spaces of all 6-dimensional real semisimple Drinfeld doubles, i.e. the sets of all possible decompositions of the Lie algebra of the Drinfeld double into Manin triples. These modular spaces are significantly different from the known one for Abelian Drinfeld double, since some of these Drinfeld doubles allow decomposition into several non-isomorphic Manin triples and their modular spaces are therefore written as unions of homogeneous spaces of different dimension. Implications for Poisson-Lie T-duality and especially Poisson-Lie T-plurality are mentioned.

Cited by

• Comments on Dualities on Group Manifolds and Supersymmetry
• Quantization of Drinfel'd doubles

Related

• CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES
• Classification of standard Manin triples in dimension 4+4
• CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS
• O(4,4) dualities and Manin triples
• Classification of 6-dimensional real Manin triples