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• W2169675714 abstract "We consider finitely generated free non-associative algebras, free commutative non-associative algebras, and free anti-commutative non-associative algebras. We study orbits of elements of these algebras under the action of automorphism groups. Using free differential calculus we obtain matrix criteria for a system of elements to have given rank (or to be primitive). It gives us a possibility to construct fast algorithm to recognize primitive systems of elements. We show that if an endomorphism of a free algebra preserves the automorphic orbit of a nonzero element, then it is an automorphism of this algebra. In particular, endomorphisms preserving primitivity of elements are automorphisms." @default.
• W2169675714 created "2016-06-24" @default.
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• W2169675714 creator A5081496738 @default.
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• W2169675714 date "2001-09-01" @default.
• W2169675714 modified "2023-10-01" @default.
• W2169675714 title "Automorphic Orbits in Free Non-associative Algebras" @default.
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• W2169675714 doi "https://doi.org/10.1006/jabr.2001.8794" @default.
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