Gelfand–Dorfman algebras, derived identities, and the Manin product of operads Full article
| Journal |
Journal of Algebra
ISSN: 0021-8693 , E-ISSN: 1090-266X |
||||||
|---|---|---|---|---|---|---|---|
| Output data | Year: 2019, Volume: 539, Pages: 260-284 Pages count : 25 DOI: 10.1016/j.jalgebra.2019.07.034 | ||||||
| Tags | Differential algebra; Gelfand–Dorfman algebra; Identity; Operad; Poisson algebra | ||||||
| Authors |
|
||||||
| Affiliations |
|
Abstract:
Gelfand–Dorfman bialgebras (GD-algebras) are nonassocia-
tive systems with two bilinear operations satisfying a series
of identities that express Hamiltonian property of an opera-
tor in the formal calculus of variations. The paper is devoted
to the study of GD-algebras related with differential Pois-
son algebras. As a byproduct, we obtain a general description
of identities that hold for operations a > b = d(a)b and
a < b = ad(b) on a (non-associative) differential algebra with
a derivation d.
Cite:
Kolesnikov P.S.
, Sartayev B.
, Orazgaliev A.
Gelfand–Dorfman algebras, derived identities, and the Manin product of operads
Journal of Algebra. 2019. V.539. P.260-284. DOI: 10.1016/j.jalgebra.2019.07.034 WOS Scopus OpenAlex
Gelfand–Dorfman algebras, derived identities, and the Manin product of operads
Journal of Algebra. 2019. V.539. P.260-284. DOI: 10.1016/j.jalgebra.2019.07.034 WOS Scopus OpenAlex
Dates:
| Published online: | Aug 13, 2019 |
Identifiers:
| Web of science: | WOS:000489677400011 |
| Scopus: | 2-s2.0-85070878878 |
| OpenAlex: | W2921364368 |