Geodesic
Growth of codimensions of metabelian algebras
Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 15-20

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We consider numerical invariants of identities of nonassociative algebras. We prove that codimension sequence of any finitely generated metabelian algebra has exponentially bounded codimension growth. It is shown that the upper PI-exponent increases at most to 1 after adjoining an external unit. For two-step left-nilpotent algebras it is proved that the lower PI-exponent increases at least to 1. 
@article{VMUMM_2017_6_a2,
     author = {M. V. Zaicev},
     title = {Growth of codimensions of metabelian algebras},
     journal = {Vestnik Moskovskogo universiteta. Matematika, mehanika},
     pages = {15--20},
     publisher = {mathdoc},
     number = {6},
     year = {2017},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a2/}
}
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M. V. Zaicev. Growth of codimensions of metabelian algebras. Vestnik Moskovskogo universiteta. Matematika, mehanika, no. 6 (2017), pp. 15-20. http://geodesic.mathdoc.fr/item/VMUMM_2017_6_a2/