On the superalgebras built from SO(3) tensor operators

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Abstract
A study is made of the superalgebra structures of the sets of SO(3) tensor operators TLM(j,j) and TLM(j,j’). It is shown that for each set of operators there exist natural splittings in two subsets that form, respectively, the even and odd parts of a superalgebra. The superalgebras built in this way are: gl(j‖j+1) for integer j, gl(j+1/2‖j+1/2) for half‐odd integer j, gl(2j+1‖2j’+1) for all j and j’, the orthosymplectic superalgebras, P(2j+1) and Q(2j+1) for all j, gl(j+j’+1‖j+j’+1) [or gl(j+j’‖j+j’+2)] for j and j’ both integers with j+j’ odd (or even) and gl(j+j’+1‖j+j’+1) for j and j’ both half‐odd integers.

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