Multialternating graded polynomials and growth of polynomial identities
By E. Aljadeff, Antonio Giambruno. 2012
64 citations recorded by the source corpus.
Let G be a finite group and A a finite dimensional G-graded algebra over a field of characteristic zero. When A is simple as a G-graded algebra, by mean of Regev central polynomials we construct multialternating graded polynomials of arbitrarily large degree non vanishing on A. As a consequence we compute the exponential rate of growth of the sequence of graded codimensions of an arbitrary G-graded algebra satisfying an ordinary polynomial identity. In particular we show it is an integer. The result was proviously known in case G is abelian.
Subfields: Algebra and Number Theory, Applied Mathematics, Geometry and Topology
View Paper: https://www.semanticscholar.org/paper/8c26cb8cf50a920358fca82b8b451b67206ed5af
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In Algebra and Number Theory
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Citations in the corpus
- Amitsur's conjecture for associative algebras with a generalized Hopf action (2012, background): “e holds for graded codimensions, G- and H-codimensions. The analog of Amitsur’s conjecture for codimensions of graded identities was proved in 2010–2011 by E. Aljadeff, A. Giambruno, and D. La Mattina [1, 2, 13] for all associative PI-algebras graded by a finite group. As a consequence, they proved th”