2021•Preprints.orgOpen access

Some Examples of Nonassociative Coalgebras and Supercoalgebras

Daniyar Kozybaev, Ualbai Umirbaev, V. N. Zhelyabin

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.

Open-access reader

About this research paper

What this paper is about

Why it matters

A significance statement is not available in the OpenAlex record.

Key contribution

A contribution statement is not available in the OpenAlex record.

Method / approach

Method details are not available in the OpenAlex metadata.

Main findings

Findings are not separately available in the OpenAlex metadata.

Limitations

Limitations are not available in the OpenAlex metadata.

Applications

Application details are not available in the OpenAlex metadata.

Available abstract

Key concepts: Coalgebra, Lie coalgebra, Mathematics, Pure mathematics, Algebra over a field, Field (mathematics), Differential (mechanical device), Novikov self-consistency principle