Simple algebras and Drinfeld doubles

Journal Article · Thu May 15 04:00:00 EDT 2008 · Physics of Atomic Nuclei

DOI:https://doi.org/10.1134/S1063778808050062· OSTI ID:21402591

Ballesteros, A ^[1]; Celeghini, E ^[2]; Olmo, M A. del, ^[3]

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1. Universidad de Burgos, Departamento de Fisica (Spain)
2. Universita di Firenze and INFN-Sezione di Firenze, Departamento di Fisica (Italy)
3. Universidad de Valladolid, Dipartimento de Fisica Teorica (Spain)

The Drinfeld double structure underlying all the Cartan series of simple Lie algebras is discussed. The two solvable algebras that allow its definition are constructed enlarging each simple algebra of rank n with a central Abelian algebra of dimension n. In these solvable algebras, isomorphic to the two Borel subalgebras, a pairing can be built. The complete machinery of Drinfeld doubles is described in all details. This offers a new approach to the explicit construction of canonical quantum deformation of simple algebras and fixes uniquely, independently and differently from known conventions, canonical bases for all of them. The Drinfeld doubles for A{sub n} and C{sub n} are explicitly written. The full quantization of su(3) is discussed in terms of standard commutators as the A{sub 2} Drinfeld double requires.

• OSTI ID: 21402591
• Journal Information: Physics of Atomic Nuclei, Journal Name: Physics of Atomic Nuclei Journal Issue: 5 Vol. 71; ISSN 1063-7788; ISSN PANUEO
• Country of Publication: United States
• Language: English

Related Subjects

71 CLASSICAL AND QUANTUM MECHANICS
GENERAL PHYSICS
ALGEBRA
COMMUTATORS
LIE GROUPS
MATHEMATICAL OPERATORS
MATHEMATICS
QUANTIZATION
QUANTUM OPERATORS
SYMMETRY GROUPS