Asymptotics of the Codimensions cn in the Algebra F(7) |
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Authors: | A. V. Grishin |
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Affiliation: | 1.Moscow State Pedagogical University,Moscow,Russia |
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Abstract: | The paper studies the additive structure of the algebra F(7), i.e., a relatively free associative countably generated algebra with the identity [x1,..., x7] = 0 over an infinite field of characteristic ≠ 2, 3. First, the space of proper multilinear polynomials in this algebra is investigated. As an application, estimates for the codimensions cn = dimFn(7) are obtained, where Fn(7) stands for the subspace of multilinear polynomials of degree n in the algebra F(7). |
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