Asymptotic behavior in Lie nilpotent relatively free algebras and extended Grassmann algebras. (English. Russian original) Zbl 1443.16025
Math. Notes 107, No. 6, 933-938 (2020); translation from Mat. Zametki 107, No. 6, 848-854 (2020).
Summary: The present paper is devoted to estimating the codimensions \(c_n\) for the variety of associative algebras given by the identity \([x_1, \dots, x_l] = 0\) for odd \(l\). The characteristic of the ground field is different from 2 and 3. The construction of the so-called extended Grassmann algebra is applied very effectively.
MSC:
| 16R10 | \(T\)-ideals, identities, varieties of associative rings and algebras |
| 17D05 | Alternative rings |
Keywords:
Lie nilpotent algebra; codimension of \(t\)-ideal; extended Grassmann algebra; measure of inclusionReferences:
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