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The classical framework for investigating the Casimir elements of a Lie algebra is generalized to the case of an ϵ Lie algebra L . We construct the standard L ‐module isomorphism of the ϵ‐symmetric algebra of L onto its enveloping algebra, and we introduce the Harish–Chandra homomorphism....
We generalize the two‐dimensional O(3) nonlinear σ‐model while preserving its conformal invariance. The integrability condition of this model encompasses the sine‐Gordon equation in addition to some special cases which are found to be of the same form. The time‐independent solutions...
We present an exactly solvable Bianchi type I cosmological model with a viscous fluid. We show that the role of viscosity is more important in the initial epochs of the universe and, in that same period, pressure is more important than fluid density.
The Dirac–Bergmann generalized Hamiltonian dynamics for a degenerate‐Lagrangian system is formulated on the Whitney sum T ∗ Q ⊕ T Q of the phase space T ∗ Q and the velocity space T Q over the configuration space Q . The formulation is related to those on T ∗ Q and T Q . Some...
We present the derivation of a useful formula for evaluating commutators of the form A , f ( B ) and f ( A ), B , where the nested commutators A , A ,⋅⋅⋅ A A , B ⋅⋅⋅ and ⋅⋅⋅ A , B , B ⋅⋅⋅, B , B do not vanish in general. The use of this formula is illustrated by a simple...
We investigate (anti‐) self‐dual Riemann space‐times for diagonal Bianchi types of class A with positive‐definite metrics. A general algorithm to find self‐dual solutions is presented. Explicit solutions are given for all types of class A.
A Racah basis is introduced for the generators of these matrix superalgebras and explicit formulas are derived for eigenvalues of Casimir operators in terms of the components of the highest weight. The result contains, as special cases, the corresponding expressions for the general linear,...
This paper considers nonclassical fields (tensor distributions) of the form τδ Ω , where δ Ω is the Dirac delta function for a moving p ‐dimensional submanifold of R n (0≤ p ≤ n ). The density τ is a classical (smooth), rank‐ k tensor field on R n +1 . The main result of the paper...
The generators of the algebras under consideration can be written in a canonical two‐index form and hence the associated standard sequence of Casimir elements can be constructed. Following the classical approach by Perelomov and Popov, we obtain the eigenvalues of these Casimir elements in an...
We develop a graded tensor calculus corresponding to arbitrary abelian groups of degrees and arbitrary commutation factors. The standard basic constructions and definitions, like tensor products, spaces of multilinear mappings, contractions, symmetrization, symmetric algebra, as well as the...
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