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- Title
THE NOWICKI CONJECTURE FOR BICOMMUTATIVE ALGEBRAS.
- Authors
FINDIK, Şehmus
- Abstract
Let K be a field of characteristic zero, and K[xn, yn] be the commutative associative unitary polynomial algebra of rank 2n generated by the set xn ? yn = {x1, ..., xn, y1, ..., yn }. It is well known that the algebra K[xn, yn]δ of constants of the locally nilpotent linear derivation δ of K[xn, yn] sending yi to xi, and xi to 0, is generated by x1, ..., xn and the determinants of the form xiyj - xj yi; that was first conjectured by Nowicki in 1994, and later proved by several authors. Bicommutative algebras are nonassociative noncommutative algebras satisfying the identities (xy)z = (xz)y and x(yz) = y(xz). In this study, we work in the 2n generated free bicommutative algebra as a noncommutative nonassociative analogue of the Nowicki conjecture, and find the generators of the algebra of constants in this algebra.
- Subjects
NONCOMMUTATIVE algebras; ALGEBRA; LOGICAL prediction; NONASSOCIATIVE algebras; POLYNOMIAL rings; POLYNOMIALS
- Publication
Eskişehir Technical University Journal of Science & Technology B - Theoretical Sciences, 2023, Vol 11, Issue 2, p104
- ISSN
2667-419X
- Publication type
Article
- DOI
10.20290/estubtdb.1200175