Cayley–klein Contractions of Orthosymplectic Superalgebras

Abstract

We define a class of orthosymplectic superalgebras osp(m; j|2n; ω) which may be obtained from osp(m|2n) by contractions and analytic continuations in a similar way as the orthogonal and the symplectic Cayley-Klein algebras are obtained from the corresponding classical ones. Contractions of osp(1|2) and osp(3|2) are regarded as an examples.

Possible quantum kinematics. II. Nonminimal case

“…The transformation of the quantum deformation parameter Z = Jv under contraction is the important ingredient of the noncommutative quantum groups and noncommutative quantum spaces. Unlike previous papers on this subject [1], [2] second power of contraction parameters are included in the multiplier J, what make all kinematics contractions admissible. The different combinations of quantum structure and Cayley-Klein scheme of contractions and analytical continuations are described with the help of permutations σ.…”

“…Therefore the analysis of a possible space-time models has the fundamental meaning for physics. In the previous papers [1], [2] the noncommutative analogs of the possible commutative kinematics [3] was constructed starting from the mathematical theory of quantum groups and quantum vector spaces [4]. Cayley-Klein scheme of contractions and analytical continuations was applied to the five dimensional q-Euclidean space.…”

“…The analysis in [1], [2] was confined to the minimal multiplier J, which has the first power multiplication of contraction parameters. This restriction imply that for certain combinations of quantum structure and Cayley-Klein scheme kinematics contractions do not exist.…”

Noncommutative space-time models

“…The reason for this definition is the simplification of expressions for commutation relations of quantum kinematics. The commutation relations of the independent generators are obtained (see [9] for details) in the form…”

“…For the permutation σ , the quantum (anti) de Sitter kinematics (9) are characterized by the fundamental time [v] = [time]. Recall that the same physical dimensions of the deformation parameter have been obtained for the quantum algebras so v (3; j; σ) and corresponding (1+1) kinematics for different permutations [10].…”