Geodesic
Codimension growth of algebras with adjoint unit
Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 11-26

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In this paper, numerical characteristics of identities of finite-dimensional nonassociative algebras are studied. Main attention is paid to the question of the change of the PI-exponent after adjoining an external unital element. We construct an example of a four-dimensional simple algebra such that its PI-exponent increases by one after adjoining an external unity. 
@article{FPM_2013_18_3_a1,
     author = {O. E. Bezushchak and A. A. Beljaev and M. V. Zaicev},
     title = {Codimension growth of algebras with adjoint unit},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {11--26},
     publisher = {mathdoc},
     volume = {18},
     number = {3},
     year = {2013},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a1/}
}
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O. E. Bezushchak; A. A. Beljaev; M. V. Zaicev. Codimension growth of algebras with adjoint unit. Fundamentalʹnaâ i prikladnaâ matematika, Tome 18 (2013) no. 3, pp. 11-26. http://geodesic.mathdoc.fr/item/FPM_2013_18_3_a1/