In this paper we consider the following family of Poisson brackets {Mi,Mj} = εijk Mk, {Mi, γj} = εijk γk, {γi, γj} = κ εijk Mk. (1.1) Here Mi and γi are components of 3-dimensional vectors M and Γ, εijk is the totally skew-symmetric tensor, κ is a parameter. It is well-known that any linear Poisson bracket is defined by an appropriate Lie algebra. The cases κ = 0, κ > 0 and κ < 0 correspond to ...

In this paper we consider the following family of Poisson brackets {Mi,Mj} = εijk Mk, {Mi, γj} = εijk γk, {γi, γj} = κ εijk Mk. (1.1) Here Mi and γi are components of 3-dimensional vectors M and Γ, εijk is the totally skew-symmetric tensor, κ is a parameter. It is well-known that any linear Poisson bracket is defined by an appropriate Lie algebra. The cases κ = 0, κ > 0 and κ < 0 correspond to ...

A $Gamma$-so-ring is a structure possessing a natural partial ordering, an infinitary partial addition and a ternary multiplication, subject to a set of axioms. The partial functions under disjoint-domain sums and functional composition is a $Gamma$-so-ring. In this paper we introduce the notions of subdirect product and $(phi,rho)$-product of $Gamma$-so-rings and study $(phi,rho)$-represen...