On the Special Identities of Gelfand–Dorfman Algebras Full article
| Journal |
Experimental Mathematics
ISSN: 1058-6458 , E-ISSN: 1944-950X |
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| Output data | Year: 2022, DOI: 10.1080/10586458.2022.2041134 | ||||
| Tags | Gelfand–Dorfman algebra; Gröbner basis; operad; Poisson algebra; special identity | ||||
| Authors |
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| Affiliations |
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Funding (1)
| 1 | Sobolev Institute of Mathematics | 0314-2019-0001 |
Abstract:
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 Gröbner basis for the corresponding shuffle operad, we show that these two identities imply all special ones up to degree 5.
Cite:
Kolesnikov P.S.
, Sartayev B.K.
On the Special Identities of Gelfand–Dorfman Algebras
Experimental Mathematics. 2022. DOI: 10.1080/10586458.2022.2041134 WOS Scopus РИНЦ OpenAlex
On the Special Identities of Gelfand–Dorfman Algebras
Experimental Mathematics. 2022. DOI: 10.1080/10586458.2022.2041134 WOS Scopus РИНЦ OpenAlex
Identifiers:
| Web of science: | WOS:000771257500001 |
| Scopus: | 2-s2.0-85126741159 |
| Elibrary: | 48193754 |
| OpenAlex: | W4302395996 |