Abstract
Let A be a PI-algebra. If A is an associative algebra, the sequence of codimensions \(c_n(A), n=1,2,\ldots ,\) of A is asymptotically non-decreasing. For the non-associative case, there are examples of PI-algebras whose sequence of codimensions is not eventually non-decreasing. For a associative PI-algebra A with involution \(*: A\rightarrow A\), it was recently shown that its sequence of \(*\)-codimensions \(c_n^*(A)\), \(n=1,2,\ldots \), is also asymptotically non-decreasing. In the present paper, we construct a non-associative algebra whose sequence of \(*\)-codimensions is not eventually non-decreasing.
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I. Shestakov was supported by the CNPq Grant 304313/2019-0 and FAPESP Grant 2018/23690-6. M. Zaicev was partially supported by FAPESP Grant 2019/02510-2 and by Russian Science Foundation Grant 16-11-10013-P.
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Shestakov, I., Zaicev, M. Eventually non-decreasing codimensions of \(*\)-identities. Arch. Math. 116, 413–421 (2021). https://doi.org/10.1007/s00013-020-01567-9
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DOI: https://doi.org/10.1007/s00013-020-01567-9