We present the classification, up to PI-equivalence, of the algebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. We also describe the generalization of this result in the setting of superalgebras and their graded identities. As a consequence we determine all linear functions describing the ordinary codimensions and the graded codimensions of a given algebra.
GIAMBRUNO A, LA MATTINA D, MISSO P (2006). On algebras and superalgebras with linear codimension growth. In Groups, Rings and Group Rings (pp.173-182). BOCA RATON, FL : Chapman & Hall/CRC.
On algebras and superalgebras with linear codimension growth
GIAMBRUNO, Antonino;LA MATTINA, Daniela;MISSO, Paola
2006-01-01
Abstract
We present the classification, up to PI-equivalence, of the algebras over a field of characteristic zero whose sequence of codimensions is linearly bounded. We also describe the generalization of this result in the setting of superalgebras and their graded identities. As a consequence we determine all linear functions describing the ordinary codimensions and the graded codimensions of a given algebra.
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