About Nilpotency of Engel Algebras

N. A. Koreshkov and D. U. Haritonov

A chapter in Formal Power Series and Algebraic Combinatorics, 2000, pp 461-467 from Springer

Abstract: Abstract In this work is proved, that anyone anticommutative Engel algebra G is nilpotent, if dim K G ≤ 4. And on the contrary, if n = dim K G > 4, then for anyone n there is example solvable Engel algebra, which is not nilpotent. Using the theorem Shirshov about height and theorem Ufnarovskii about independence state two sufficient conditions of a nilpotency of anticom­mutative algebra G. This conditions state in the terms of an associative algebra A(G), generated by operators of the right multiplication.

Date: 2000
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DOI: 10.1007/978-3-662-04166-6_43

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