Some examples of nonassociative coalgebras and supercoalgebras

  title={Some examples of nonassociative coalgebras and supercoalgebras},
  author={Daniyar Kozybaev and Ualbai U. Umirbaev and Viktor Zhelyabin},
  journal={Linear Algebra and its Applications},
1 Citations
On the Lie-solvability of Novikov algebras
We prove that any Novikov algebra over a field of characteristic [Formula: see text] is Lie-solvable if and only if its commutator ideal [Formula: see text] is right nilpotent. We also construct


The Kantor-Koecher-Tits construction for Jordan coalgebras
The relationship between Jordan and Lie coalgebras is established. We prove that from any Jordan coalgebra 〈L(A), Δ〉, it is possible to construct a Lie coalgebra 〈L(A), ΔL〉. Moreover, any dual
Dual Coalgebras of Jordan Bialgebras and Superalgebras
W. Michaelis showed for Lie bialgebras that the dual coalgebra of a Lie algebra is a Lie bialgebra. In the present article we study an analogous question in the case of Jordan bialgebras. We prove
Locally finite coalgebras and the locally nilpotent radical II
Abstract In this article, we describe a criterion for an element of the dual space of an algebra to belong to the finite dual. This result is used to study when a certain subspace of the dual space
Locally finite coalgebras and the locally nilpotent radical I
Jordan (Super)Coalgebras and Lie (Super)Coalgebras
We discuss the question of local finite dimensionality of Jordan supercoalgebras. We establish a connection between Jordan and Lie supercoalgebras which is analogous to the Kantor–Koecher–Tits
Embedding of Jordan Copairs into Lie Coalgebras
Let (V, Δ) be a Jordan copair over a field Φ and let V* be its dual pair. Then there exists a Lie coalgebra (L c (V), Δ L ) whose dual algebra (L c (V))* is the Kantor–Koecher–Tits construction for
Mikheev’s construction for Mal’tsev coalgebras
In [1-3], a relationship was established between Moufang loops and groups on which automorphisms of a special form act (groups with triality). The relationship turned out useful for studying
Embedding Mal’tsev Coalgebras into Lie Coalgebras with Triality
It is proved that any Mal’tsev coalgebra embeds in a Lie coalgebra with triality. Thus Mikheev’s known result for Mal’tsev algebras is fully extended to Mal’tsev coalgebras.
An example of a non-zero Lie coalgebra M for which Loc(M)=0
Identities of the left-symmetric Witt algebras
All right operator identities of ℒn are described and it is proved that the set of all algebras �°n, where n ≥ 1, generates the variety of all left-symmetric algebraes.