Symmetric polynomials in the free metabelian Poisson algebras

Dushimirimana A., Flndlk Ş., Öǧüşlü N. Ş.

Journal of Algebra and its Applications, cilt.22, sa.2, 2023 (SCI-Expanded, Scopus) identifier

  • Yayın Türü: Makale / Tam Makale
  • Cilt numarası: 22 Sayı: 2
  • Basım Tarihi: 2023
  • Doi Numarası: 10.1142/s0219498823500494
  • Dergi Adı: Journal of Algebra and its Applications
  • Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, Academic Search Premier, Aerospace Database, Communication Abstracts, MathSciNet, Metadex, zbMATH, Civil Engineering Abstracts
  • Anahtar Kelimeler: Lie algebras, Poisson algebras, symmetric polynomials
  • Çukurova Üniversitesi Adresli: Evet

Özet

Let K be a field of characteristic zero and Xn = {x1,...,xn} be a finite set of variables. Consider the free metabelian Poisson algebra Pn of rank n generated by Xn over K. An element in Pn is called symmetric if it is preserved under any change of variables, i.e. under the action of each permutation in Sn. In this study, we determine the algebra PnSn of symmetric polynomials of Pn.