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Symmetric powers of Nat SL(2,𝕂)

  • Adrien Deloro EMAIL logo
Published/Copyright: January 14, 2016
Journal of Group Theory
From the journal Journal of Group Theory Volume 19 Issue 4

Abstract

In this paper, we identify the representations 𝕂⁢[Xk,Xk-1⁢Y,…,Yk] among abstract ℤ⁢[SL2⁡(𝕂)]-modules. One result is on ℚ⁢[SL2⁡(ℤ)]-modules of nilpotence length at most 5 and generalises a classical “quadratic” theorem by Smith and Timmesfeld; there are reasons to believe that this generalisation is close to optimal. Another result is on extending the linear structure on the module from the prime field to 𝕂. All proofs are by computation in the group ring using the Steinberg relations.

References

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Received: 2015-4-30
Revised: 2015-10-1
Published Online: 2016-1-14
Published in Print: 2016-7-1

© 2016 by De Gruyter

Articles in the same Issue

  1. Frontmatter
  2. Codegrees and nilpotence class of p-groups
  3. On finite 2-equilibrated p-groups
  4. Minimal dimension of faithful representations for p-groups
  5. On the Christensen–Wang bounds for the ghost number of a p-group algebra
  6. A family of non-Schurian p-Schur rings over groups of order p3
  7. Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
  8. Symmetric powers of Nat SL(2,𝕂)
  9. Nested GVZ-groups
  10. On some groups generated by involutions
  11. Thompson’s conjecture for finite simple groups of Lie type Bn and Cn
https://doi.org/10.1515/jgth-2015-0049

Articles in the same Issue

  1. Frontmatter
  2. Codegrees and nilpotence class of p-groups
  3. On finite 2-equilibrated p-groups
  4. Minimal dimension of faithful representations for p-groups
  5. On the Christensen–Wang bounds for the ghost number of a p-group algebra
  6. A family of non-Schurian p-Schur rings over groups of order p3
  7. Endo-trivial modules for finite groups with dihedral Sylow 2-subgroup
  8. Symmetric powers of Nat SL(2,𝕂)
  9. Nested GVZ-groups
  10. On some groups generated by involutions
  11. Thompson’s conjecture for finite simple groups of Lie type Bn and Cn
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