Nonassociative algebras related to Hamiltonian operators in the formal calculus of variations
An algebra is called Novikov if it satisfies the identities \((xy)z= (xz)y\) and \((x, y, z)= (y, x, z)\). Let \(A\) be a simple Novikov algebra over an algebraically closed field, and suppose \(A\) contains a maximal subalgebra \(H\) such that \(A/H\) has a finite-dimensional irreducible \(H\)-submodule. Such an algebra has a Weisfeiler filtration which leads to a graded algebra \(G\) associated with \(A\). The authors show that the algebra \(G\) has to be one of four types. Furthermore, the codimension of \(H\) is finite only for one of these types, and in this case it is 1. For \(A^*\) the closure of \(A\) with respect to the topology induced by the filtration, it is also shown that \(A^*= G^*\) for three of these types, assuming a certain added restriction for one of them.
scientific article; zbMATH DE number 802566
scientific article