2018/12/30 by P. S. Kolesnikov, Kolesnikov, P. S.
Mathematics · #Advanced Topics in Algebra #Algebraic structures and combinatorial models #FOS: Mathematics #Homotopy and Cohomology in Algebraic Topology #Quantum Algebra (math.QA)
paper · pdf · doi:10.48550/arxiv.1812.11516
openalex publication_date 2018/12/30 · openalex created_date 2025/10/10 · openalex updated_date 2026/07/28
Suppose A is a not necessarily associative algebra with a derivation d. Then A may be considered as a system with two binary operations \succ and \prec defined by x\succ y = d(x)y, x\prec y = xd(y), x,y∈ A. Suppose A satisfies some multi-linear polynomial identities. We show how to find the identities that hold for operations \prec and \succ . It turns out that if A belongs to a variety governed by an operad Var then \succ and \prec satisfy the defining relations of the operad Var∘ Nov, where ∘ is the Manin white product of operads, Nov is the operad of Novikov algebras. Moreover, there are no other identities that hold for operations \succ , \prec on an arbitrary differential Var-algebra.