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Free nonassociative supercommutative algebras. (Russian, English) Zbl 1072.17002
Fundam. Prikl. Mat. 9, No. 3, 103-109 (2003); translation in J. Math. Sci., New York 135, No. 5, 3336-3340 (2006).
A free nonassociative supercommutative algebra \(A\) on the alphabets \(X\) and \(Y\) over a field \(F\) is a factor-algebra of the free nonassociative algebra over \(F\) on the alphabet \(X\coprod Y\) on the ideal generated by all identities of type \(uv=-\delta vu\), here \(\delta=-1\) if \(u,v\) are both odd and \(\delta=1\) otherwise. It is proved that homogeneous subalgebras of free nonassociative supercommutative algebras are free. As a consequence, it is shown that the group of automorphisms of a free nonassociative supercommutative algebras is generated by elementary automorphisms.

17A50 Free nonassociative algebras