Some examples of nonassociative coalgebras and supercoalgebras
Kozybaev D. Umirbaev U. Zhelyabin V.
15 June 2022Elsevier Inc.
Linear Algebra and Its Applications
2022#643235 - 257 pp.
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.
Coalgebra , Coderivation , Jordan superalgebra , Lie algebra , Novikov algebra , Right-alternative algebra
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Department of Mathematics, Eurasian National University, Nur-Sultan, Kazakhstan
Department of Mathematics, Wayne State University, Detroit, 48202, MI, United States
Department of Mathematics, Al-Farabi Kazakh National University, Almaty, 050040, Kazakhstan
Institute of Mathematics and Mathematical Modeling, Almaty, 050010, Kazakhstan
Institute of Mathematics of the SB of RAS, Novosibirsk, 630090, Russian Federation
Department of Mathematics
Department of Mathematics
Department of Mathematics
Institute of Mathematics and Mathematical Modeling
Institute of Mathematics of the SB of RAS
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