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PreprintCC BY 4.0arXiv

Polynomial identities, central polynomials and cocharacters of M2(F) with transpose superinvolution

  • Rafael Bezerra dos Santos
  • Lucas Reis
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Abstract

Let F be a field of characteristic zero and consider M2(F), the algebra of 2× 2 matrices over F, with canonical ℤ2-grading and endowed with transpose superinvolution. In this paper, we present the generators of the T2*-ideal of *-identities and of the T2*-subspace of central *-polynomials of M2(F). As a consequence, we determine the sequences of *-codimensions and ⟨ n⟩-cocharacters of M2(F). In particular, we prove that the n-th *-codimension grows like 4nn−1/2.

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Cite

BibTeXRIS
BibTeX
@misc{santos2026polynomial,
  title = {{Polynomial identities, central polynomials and cocharacters of $M_2(F)$ with transpose superinvolution}},
  author = {Rafael Bezerra dos Santos and Lucas Reis},
  howpublished = {arXiv},
  year = {2026},
  month = sep,
  doi = {10.48550/arxiv.2609.20458},
  eprint = {2609.20458},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2609.20458},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Polynomial identities, central polynomials and cocharacters of M_2(F) with transpose superinvolution
AU  - Rafael Bezerra dos Santos
AU  - Lucas Reis
PY  - 2026
DA  - 2026/09/17
PB  - arXiv
DO  - 10.48550/arxiv.2609.20458
UR  - https://arxiv.org/abs/2609.20458
AB  - Let F be a field of characteristic zero and consider M_2(F), the algebra of 2× 2 matrices over F, with canonical ℤ_2-grading and endowed with transpose superinvolution. In this paper, we present the generators of the T_2^*-ideal of *-identities and of the T_2^*-subspace of central *-polynomials of M_2(F). As a consequence, we determine the sequences of *-codimensions and ⟨ n⟩-cocharacters of M_2(F). In particular, we prove that the n-th *-codimension grows like 4^nn^−1/2.
ER  -