Abstract:
Locally finiteness of some varieties of nonassociative coalgebras is studied and the Gelfand-Dorfman construction for
Novikov coalgebras and the Kantor construction for Jordan
super-coalgebras are given. We give examples of a non-locally
finite differential coalgebra, Novikov coalgebra, Lie coalgebra,
Jordan super-coalgebra, and right-alternative coalgebra. The
dual algebra of each of these examples satisfies very strong additional identities. We also constructed examples of an infinite
dimensional simple differential coalgebra, Novikov coalgebra,
Lie coalgebra, and Jordan super-coalgebra over a field of characteristic zero.
