Modular invariants of finite gluing groups
| Autor: | R. James Shank, David L. Wehlau, Yin Chen |
|---|---|
| Rok vydání: | 2021 |
| Předmět: |
Classical group
Semidirect product Pure mathematics Algebra and Number Theory Symplectic group 010102 general mathematics Sylow theorems Field of fractions 13A50 Mathematics - Commutative Algebra Commutative Algebra (math.AC) 01 natural sciences Faithful representation Mathematics::Group Theory QA150 0103 physical sciences FOS: Mathematics 010307 mathematical physics Representation Theory (math.RT) 0101 mathematics Abelian group Invariant (mathematics) Mathematics - Representation Theory Mathematics |
| Zdroj: | Journal of Algebra. 566:405-434 |
| ISSN: | 0021-8693 |
| DOI: | 10.1016/j.jalgebra.2020.08.034 |
| Popis: | We use the gluing construction introduced by Jia Huang to explore the rings of invariants for a range of modular representations. We construct generating sets for the rings of invariants of the maximal parabolic subgroups of a finite symplectic group and their common Sylow $p$-subgroup. We also investigate the invariants of singular finite classical groups. We introduce parabolic gluing and use this construction to compute the invariant field of fractions for a range of representations. We use thin gluing to construct faithful representations of semidirect products and to determine the minimum dimension of a faithful representation of the semidirect product of a cyclic $p$-group acting on an elementary abelian $p$-group. Comment: Example 5.12 has been corrected and expanded |
| Databáze: | OpenAIRE |
| Externí odkaz: |
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