Free color Lie super-rings. (English. Russian original) Zbl 0744.17033

Sov. Math. 35, No. 10, 42-44 (1991); translation from Izv. Vyssh. Uchebn. Zaved., Mat. 1991, No. 10(353), 46-49 (1991).
The author proves analogs of the theorems of E. Witt and A. I. Shirshov for color Lie superalgebras. Namely, he proves the following results: (i) Any Lie superalgebra (or Lie \(p\)-superalgebra) of at most countable rank over a field of characteristic \(\neq 2,3\) can be embedded into a Lie superalgebra (or \(p\)-superalgebra) with two generators over the same field; (ii) Let \(K\) be a commutative domain over which all projective modules are free, \(L\) be the free \(K\)-operator color Lie (\(p\)-) super- ring and \(B\) be an isolated \(G\)-homogeneous subring of \(L\). If \(B\) is a direct summand of the \(K\)-module \(L\) then \(B\) is a free \(K\)-operator color Lie (\(p\)-) super-ring.
There is also the analog of P. M. Cohn’s criterion (for identical relations among left normed monomials in Lie rings) for free color Lie super-rings.


17B70 Graded Lie (super)algebras
17A70 Superalgebras