Preprint Article Version 1 Preserved in Portico This version is not peer-reviewed

Some Examples of Nonassociative Coalgebras and Supercoalgebras

Version 1 : Received: 28 November 2021 / Approved: 29 November 2021 / Online: 29 November 2021 (11:35:43 CET)

How to cite: Kozybaev, D.; Umirbaev, U.; Zhelyabin, V. Some Examples of Nonassociative Coalgebras and Supercoalgebras. Preprints 2021, 2021110522 (doi: 10.20944/preprints202111.0522.v1). Kozybaev, D.; Umirbaev, U.; Zhelyabin, V. Some Examples of Nonassociative Coalgebras and Supercoalgebras. Preprints 2021, 2021110522 (doi: 10.20944/preprints202111.0522.v1).

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.

Keywords

coalgebra; coderivation; differential algebra; Novikov algebra; Lie algebra; Jordan superalgebra; right-alternative algebra

Subject

MATHEMATICS & COMPUTER SCIENCE, Algebra & Number Theory

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