CONSTANTS OF PARTIAL DERIVATIONS AND PRIMITIVE OPERATIONS

Author(s)

Pchelintsev, S. V. ^{[1, 2]} ; Shestakov, I. P. ^{[3, 1, 4]}

Affiliation

^[1] Sobolev Inst Math, Pr Akad Koptyuga 4, Novosibirsk 630090 - Russia

^[2] Govt Russian Federat, Finance Acad, Leningradskii Pr 49, Moscow 125993 - Russia

^[3] Univ Sao Paulo, BR-05315970 Sao Paulo - Brazil

^[4] Novosibirsk State Univ, Ul Pirogova 1, Novosibirsk 630090 - Russia

• Document type: Journal article
• Source: Algebra and Logic; v. 56, n. 3, p. 210-231, JUL 2017.
• Web of Science Citations: 1

Abstract

We describe algebras of constants of the set of all partial derivations in free algebras of unitarily closed varieties over a field of characteristic 0. These constants are also called proper polynomials. It is proved that a subalgebra of proper polynomials coincides with the subalgebra generated by values of commutators and Umirbaev-Shestakov primitive elements p(m,n) on a set of generators for a free algebra. The space of primitive elements is a linear algebraic system over a signature Sigma = [{[} x, y], p(m,n) vertical bar m, n >= 1]. We point out bases of operations of the set S in the classes of all algebras, all commutative algebras, right alternative and Jordan algebras. (AU)

• FAPESP's process: 14/09310-5 - Algebraic structures and their representations
• Grantee: Vyacheslav Futorny
• Support Opportunities: Research Projects - Thematic Grants