Some examples of nonassociative coalgebras and supercoalgebras
Rings and Algebras
2021-11-30 v1 Quantum Algebra
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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Cite
@article{arxiv.2111.13765,
title = {Some examples of nonassociative coalgebras and supercoalgebras},
author = {Daniyar Kozybaev and Ualbai Umirbaev and Viktor Zhelyabin},
journal= {arXiv preprint arXiv:2111.13765},
year = {2021}
}
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19 pages