CLASSIFICATION OF SIX-DIMENSIONAL REAL DRINFELD DOUBLES

2002/02/28 by L. Snobl, LIBOR ŠNOBL, L. Hlavaty +1 · 9 citations
Mathematics · Physics and Astronomy · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #Homotopy and Cohomology in Algebraic Topology #hep-th #math-ph #math.MP #math.QA

paper · pdf · doi:10.1142/s0217751x02010571

published as Int.J.Mod.Phys. A17 (2002) 4043-4068 · 27 pages, corrected minor mistakes and typos, added references

arxiv created 2002/03/27 · openalex publication_date 2002/11/07 · arxiv updated 2009/11/30 · openalex created_date 2016/06/24 · openalex updated_date 2026/07/28

Abstract

Starting from the classification of real Manin triples we look for those that are isomorphic as six-dimensional Drinfeld doubles i.e. Lie algebras with the ad-invariant form used for construction of the Manin triples. We use several invariants of the Lie algebras to distinguish the nonisomorphic structures and give the explicit form of maps between Manin triples that are decompositions of isomorphic Drinfeld doubles. The result is a complete list of six-dimensional real Drinfeld doubles. It consists of 22 classes of nonisomorphic Drinfeld doubles.

Citations

• CLASSIFICATION OF POISSON–LIE T-DUAL MODELS WITH TWO-DIMENSIONAL TARGETS

Cited by

• O(4,4) dualities and Manin triples
• Classification of standard Manin triples in dimension 4+4
• Non-Abelian target space duals of Thurston geometries
• Dressing cosets revisited
• T-dualization of Gödel string cosmologies via Poisson–Lie T-duality approach
• One-loop renormalizability of all 2-dimensional Poisson–Lie σ-models
• Effective Actions for σ‐Models of Poisson–Lie Type
• Comments on η-deformed principal chiral model from 4D Chern-Simons theory
• Quantization of Drinfel'd doubles

Related

• Classification of 6-dimensional real Manin triples
• Classification of standard Manin triples in dimension 4+4
• On modular spaces of semisimple Drinfeld doubles
• Manin triples of real simple Lie algebras. Part 1
• Manin triples of real simple Lie algebras. Part 2