On group gradings on PI-algebras

Eli Aljadeff; Ofir David

doi:10.1016/j.jalgebra.2014.12.042

paper

On group gradings on PI-algebras

arXiv:1403.0200 · doi:10.1016/j.jalgebra.2014.12.042

Abstract

We show that there exists a constant K such that for any PI- algebra W and any nondegenerate G-grading on W where G is any group (possibly infinite), there exists an abelian subgroup U of G with $[G : U] \leq e x p (W)^{K}$ . A G-grading $W = ⨁_{g \in G} W_{g}$ is said to be nondegenerate if $W_{g_{1}} W_{g_{2}} ... W_{g_{r}} \neq = 0$ for any $r \geq 1$ and any $r$ tuple $(g_{1}, g_{2}, ..., g_{r})$ in $G^{r}$ .

17 pages

On group gradings on PI-algebras

Abstract

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