On the Special Identities of Gelfand-Dorfman Algebras
EXPERIMENTAL MATHEMATICS, cilt.33, sa.1, ss.165-174, 2024 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 33 Sayı: 1
- Basım Tarihi: 2024
- Doi Numarası: 10.1080/10586458.2022.2041134
- Dergi Adı: EXPERIMENTAL MATHEMATICS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus, MathSciNet, zbMATH
- Sayfa Sayıları: ss.165-174
- Anahtar Kelimeler: Gelfand-Dorfman algebra, Poisson algebra, special identity, Grobner basis, operad, BASES
- Süleyman Demirel Üniversitesi Adresli: Hayır
Özet
A Gelfand-Dorfman algebra (GD-algebra) is said to be special if it can be embedded into a differential Poisson algebra. In this paper, we prove that the class of all special GD-algebras is closed with respect to homomorphisms and thus forms a variety. We describe a technique for finding potentially all special identities of GD-algebras and derive two known special identities of degree 4 in this way. By computing the Grobner basis for the corresponding shuffle operad, we show that these two identities imply all special ones up to degree 5.