Abstract
We study ℤ2-graded identities of Lie superalgebras of the type b(t), t ≥ 2, over a field of characteristic zero. Our main result is that the n-th codimension is strictly less than \((\dim b(t))^n\) asymptotically. As a consequence we obtain an upper bound for ordinary (non-graded) PI-exponent for each simple Lie superalgebra b(t), t ≥ 3.
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The first author was supported by the Slovenian Research Agency grants P1-0292-0101 and J1-4144-0101. The second author was partially supported by RFBR, grant 13-01-00234a. We thank the referee for comments and suggestions.
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Repovš, D., Zaicev, M. Graded Identities of Some Simple Lie Superalgebras. Algebr Represent Theor 17, 1401–1412 (2014). https://doi.org/10.1007/s10468-013-9453-8
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DOI: https://doi.org/10.1007/s10468-013-9453-8