Some Examples of Nonassociative Coalgebras and Supercoalgebras
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This paper investigates locally finiteness of nonassociative coalgebras, presents Gelfand-Dorfman and Kantor constructions, and provides examples of various non-locally finite and infinite dimensional simple coalgebras.
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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.
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- europepmc
- last seen: 2026-05-19T01:45:01.086888+00:00