Images of Golod-Shafarevich algebras with small growth

Details Images of Golod-Shafarevich algebras with small growth Images of Golod-Shafarevich algebras with small growth

2011-08-22

arxiv.org/abs/1108.4267v1

Mathematics

Rings and Algebras

Scientific paper

We show that Golod-Shafarevich algebras can be homomorphically mapped onto infinite-dimensional algebras with polynomial growth, under mild assumptions of the number of relations of given degrees. In case these algebras are finitely presented, we show they can be mapped onto an infinite dimensional algebras with quadratic growth. This answers a guestion by Zelmanov. We then show, by an elementary construction, that any sufficiently regular function at least $n^{\log n}$ may occur as the growth of an algebra.

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