Work

Classification of Standard Manin Triples in Dimension 4+4

Year: 2025

Type: article

Abstract: Four- and six-dimensional Drinfeld doubles were classified in the past in terms of Manin triples. We provide an important step toward the classification of eight-dimensional Drinfeld doubles by presenting an extensive list of Manin triples formed by pairs of four–dimensional Lie algebras. Due to the high complexity of the classification we focus on Manin triples formed by algebras in a certain standard form. The list contains 188 nonisomorphic Manin triples plus their duals. To apply the results, we construct several four-dimensional Wess–Zumino–Witten (WZW) models on non-semisimple Lie groups. Some of the WZW models are known from the literature, but new cases are presented as well. As a consequence of the construction method, the WZW models are Poisson–Lie dualizable.

Source: Progress of Theoretical and Experimental Physics

DOI: 10.1093/ptep/ptaf154

Authors: Ladislav Hlavatý, Petr Novotný, Ivo Petr

Institution: Czech Technical University in Prague

Language: English

Topic: Advanced Topics in Algebra

Subfield: Algebra and Number Theory

Field: Mathematics

Domain: Physical Sciences

Open Access status: gold

Estimated APC paid: $979

Funder: Sponsoring Consortium for Open Access Publishing in Particle Physics