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Free nonassociative supercommutative algebras

Abstract

In the present work, we prove that homogeneous subalgebras of free nonassociative supercommutative algebras are free. As a consequence, we show that the group of automorphisms of a free nonassociative supercommutative algebra of finite rank is generated by elementary automorphisms.

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Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 9, No. 3, pp. 103–109, 2003.

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Korepanov, A.I. Free nonassociative supercommutative algebras. J Math Sci 135, 3336–3340 (2006). https://doi.org/10.1007/s10958-006-0162-2

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Keywords

  • Finite Rank
  • Elementary Automorphism
  • Supercommutative Algebra