2025/02/05 by Iritan Ferreira dos Santos, Santos, Iritan Ferreira dos, Alexey Kuz'min +3 · 2 citations
Mathematics · #17A30 #17A50 #17D25 #17D99 #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Rings and Algebras (math.RA)
paper · pdf · doi:10.48550/arxiv.2502.03184
openalex publication_date 2025/02/05 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Polynomial identities of two-dimensional Novikov algebras are studied over the complex field ℂ. We determine minimal generating sets for the T-ideals of the polynomial identities and linear bases for the corresponding relatively free algebras. As a consequence, we establish that polynomial identities separate two-dimensional Novikov algebras, which are not associative. Namely, any two-dimensional Novikov algebras, which are not associative, are isomorphic if and only if they satisfy the same polynomial identities. Moreover, we obtain the codimension sequences of all these algebras. In particular, every two-dimensional Novikov algebra has at most linear growth of its codimension sequence. We explicitly describe multilinear images of every two-dimensional Novikov algebra. In particular, we show that these images are vector spaces.