Let K be a field of characteristic 0 and L be a G-graded Lie PI-algebra where the support of L is a finite subset of G. We define the G-graded Gelfand–Kirillov dimension (GK) of L in k-variables as the GK dimension of its G-graded relatively free algebra having k homogeneous variables for each element of the support of L. We compute the G-graded GK dimension of sl2(K), where G is any abelian group. Then, we compute the exact value for the Zn -graded GK dimension of sln(K) endowed with the Zn -grading of Vasilovsky.
On the growth of graded polynomial identities of
Centrone L.
;
2017-01-01
Abstract
Let K be a field of characteristic 0 and L be a G-graded Lie PI-algebra where the support of L is a finite subset of G. We define the G-graded Gelfand–Kirillov dimension (GK) of L in k-variables as the GK dimension of its G-graded relatively free algebra having k homogeneous variables for each element of the support of L. We compute the G-graded GK dimension of sl2(K), where G is any abelian group. Then, we compute the exact value for the Zn -graded GK dimension of sln(K) endowed with the Zn -grading of Vasilovsky.File in questo prodotto:
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