REPRESENTABILITY AND SPECHT PROBLEM FOR G-GRADED ALGEBRAS

By E. Aljadeff, A. Kanel’-Belov. 2009

96 citations recorded by the source corpus.

Abstract Let W be an associative PI-algebra over a field F of characteristic zero, graded by a finite group G. Let id G ( W ) denote the T-ideal of G-graded identities of W. We prove: 1. [G-graded PI-equivalence] There exists a field extension K of F and a finite-dimensional Z / 2 Z × G -graded algebra A over K such that id G ( W ) = id G ( A ∗ ) where A ∗ is the Grassmann envelope of A. 2. [G-graded Specht problem] The T-ideal id G ( W ) is finitely generated as a T-ideal. 3. [G-graded PI-equivalence for affine algebras] Let W be a G-graded affine algebra over F. Then there exists a field extension K of F and a finite-dimensional algebra A over K such that id G ( W ) = id G ( A ) .

Subfields: Algebra and Number Theory, Geometry and Topology, Mathematical Physics

View Paper: https://www.semanticscholar.org/paper/fcc98db08bc7d398e935b6572a92769eb8fddc54

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In Algebra and Number Theory

1. E. Aljadeff
2. Antonio Giambruno
3. Alexey Gordienko

In Geometry and Topology

1. Antonio Giambruno
2. E. Aljadeff
3. Alexey Gordienko

In Mathematical Physics

1. Antonio Giambruno
2. E. Aljadeff

Citations in the corpus

• Multialternating graded polynomials and growth of polynomial identities (2012, background): “In fact, by a result of Aljadeff and Belov ([2]), any variety of G-graded PI-algebras can be generated by the Grassmann envelope of a suitable finite dimensional G×Z2-graded algebra.”