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PreprintCC BY 4.0arXiv

Polynomial identities, central polynomials and cocharacters of M2(F) with G-graded involution

  • Rafael Bezerra dos Santos
  • Lucas Reis
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Abstract

Let F be a field of characteristic zero, G be a finite abelian group and M2(F) be the algebra of 2× 2 matrices over F. In this paper, we consider all G-graded involutions on M2(F) and determine the generators of the T(G,*)-ideal of identities and of the T(G,*)-space of central polynomials of M2(F). Moreover, we explicitly compute the ⟨ n⟩-cocharacter and the n-th $(G, *)$-codimensions for most of the gradings. For the case of gradings by the Klein group, the $(G, *)$-central codimensions and proper central $(G, *)$-codimensions are also explicitly computed.

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Cite

BibTeXRIS
BibTeX
@misc{santos2026polynomial,
  title = {{Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with $G$-graded involution}},
  author = {Rafael Bezerra dos Santos and Lucas Reis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20488},
  eprint = {2609.20488},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20488},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Polynomial identities, central polynomials and cocharacters of M_2(F) with G-graded involution
AU  - Rafael Bezerra dos Santos
AU  - Lucas Reis
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20488
UR  - https://arxiv.org/abs/2609.20488
AB  - Let F be a field of characteristic zero, G be a finite abelian group and M_2(F) be the algebra of 2× 2 matrices over F. In this paper, we consider all G-graded involutions on M_2(F) and determine the generators of the T_(G,*)-ideal of identities and of the T_(G,*)-space of central polynomials of M_2(F). Moreover, we explicitly compute the ⟨ n⟩-cocharacter and the n-th $(G, *)$-codimensions for most of the gradings. For the case of gradings by the Klein group, the $(G, *)$-central codimensions and proper central $(G, *)$-codimensions are also explicitly computed.
ER  -