Dihedral invariants in the variety of upper triangular matrices
Rendiconti del Circolo Matematico di Palermo, cilt.75, sa.5, 2026 (ESCI, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 75 Sayı: 5
- Basım Tarihi: 2026
- Doi Numarası: 10.1007/s12215-026-01443-5
- Dergi Adı: Rendiconti del Circolo Matematico di Palermo
- Derginin Tarandığı İndeksler: Emerging Sources Citation Index (ESCI), Scopus, MathSciNet, zbMATH, DIALNET, Materials Science & Engineering Collection (ProQuest), Technology Collection (ProQuest)
- Anahtar Kelimeler: Dihedral group, Noncommutative invariant theory, Upper triangular matrices
- Çukurova Üniversitesi Adresli: Evet
Özet
Let Uk(C) be the unitary associative algebra of k×k upper triangular matrices with entries from the field C of complex numbers, and Fk=F(Uk(C)) be the free algebra of rank 2 generated by the set {u,v} in the variety generated by Uk(C). The algebra Fk satisfies the polynomial identity [x1,x2]⋯[x2k-1,x2k]=0. The dihedral group D2n=⟨ρ,τ∣ρn=τ2=(τρ)2=1⟩ acts on Fk as ρ(u)=e2πinu, ρ(v)=e-2πinv, τ(u)=v, τ(v)=u. In this study, we provide a generating set for the algebra FkD2n of invariants of D2n. We also compute the Hilbert series H(FkD2n,t) of FkD2n for k=3,4.