Non-standard quantum so(3,2) and its contractions

Abstract

A full (triangular) quantum deformation of so(3,2) is presented by considering this algebra as the conformal algebra of the 2+1 dimensional Minkowskian spacetime. Non-relativistic contractions are analysed and used to obtain quantum Hopf structures for the conformal algebras of the 2+1 Galilean and Carroll spacetimes. Relations between the latter and the null-plane quantum Poincaré algebra are studied.

9 pages, LaTeX

References in corpus (6)

• A New Null-Plane Quantum Poincare Algebra
• Lie bialgebra contractions and quantum deformations of quasi-orthogonal algebras
• Non-standard quantum so(2,2) and beyond
• Null-plane Quantum Universal $R$-matrix
• Quantum Deformations of Conformal Algebras Introducing Fundamental Mass Parameters
• (2+1) null-plane quantum Poincaré group from a factorized universal $R$-matrix

Cited by in corpus (10)

• κ-deformations of D=4 Weyl and conformal symmetries
• Non-commutative relativistic spacetimes and worldlines from 2+1 quantum (anti-)de Sitter groups
• Jordanian Quantum Deformations of D=4 Anti-de-Sitter and Poincare Superalgebras
• New quantum (anti)de Sitter algebras and discrete symmetries
• A new Doubly Special Relativity theory from a quantum Weyl-Poincare algebra
• $\kappa$-deformations of D=3 conformal versus deformations of D=4 AdS symmetries
• New time-type and space-type non-standard quantum algebras and discrete symmetries
• Twisted Conformal Algebra so(4,2)
• Deformation of orthosymplectic Lie superalgebra osp(1|2)
• Twist of Lie algebras by 6 dimensional subalgebra