Free special Gelfand-Dorfman algebra
V. Gubarev, B. K. Sartayev
TL;DR
This paper introduces a new basis for free Novikov algebras and uses it to construct a monomial basis for free special Gelfand-Dorfman algebras, advancing understanding of their algebraic structure.
Contribution
It provides a new basis for free Novikov algebras and constructs a monomial basis for free special Gelfand-Dorfman algebras, which was not previously known.
Findings
New basis of the free Novikov algebra
Construction of the monomial basis of free special Gelfand-Dorfman algebra
Enhanced understanding of algebraic structure of these algebras
Abstract
A Gelfand-Dorfman algebra is called special if it can be embedded into a differential Poisson algebra. We find a new basis of the free Novikov algebra. With its help, we construct the monomial basis of the free special Gelfand-Dorfman algebra.
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Taxonomy
TopicsAdvanced Topics in Algebra · Algebraic structures and combinatorial models · Advanced Combinatorial Mathematics