The Construction of the Base of the AlternativeSuperalgebra of Index 3

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F68407700%3A21230%2F09%3A00159169" target="_blank" >RIV/68407700:21230/09:00159169 - isvavai.cz</a>
Result on the web
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DOI - Digital Object Identifier
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Result language
angličtina
Original language name
The Construction of the Base of the AlternativeSuperalgebra of Index 3
Original language description
The classical Dubnov-Ivanov-Nagata-Higman theorem states that in characteristic zero every associative nil-algebra of index n is nilpotent. It turns out that, in contrast to the associative case, alternative nil-algebras of bounded index can be non-nilpotent, that is, the Dubnov-Ivanov-Nagata-Higman theorem does not carry over to alternative algebras. This was proved by Dorofeev who constructed an example of a solvable alternative algebra which is not nilpotent. Zhevlakov's theorem establishes that in characteristic zero every alternative nil-algebra of index n is solvable. It would be interesting to obtain a better estimate for the index of solvability of alternative nil-algebras. Recall, that no base of the free alternative algebra is known. Here weuse the base of the free alternative superalgebra on one odd generator x to compute its solvability index which is 3.
Czech name
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Czech description
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Project
<a href="/en/project/KJB101210801" target="_blank" >KJB101210801: Superalgebra approach for free algebras</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2009
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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