## One Citation

On the Lie-solvability of Novikov algebras

- Mathematics
- 2021

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…

## References

SHOWING 1-10 OF 31 REFERENCES

The Kantor-Koecher-Tits construction for Jordan coalgebras

- Mathematics
- 1996

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

- Mathematics
- 2005

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

- MathematicsCommunications in Algebra
- 2021

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

- MathematicsLinear Algebra and its Applications
- 2021

Jordan (Super)Coalgebras and Lie (Super)Coalgebras

- Mathematics
- 2003

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

- Mathematics
- 2007

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

- Mathematics
- 2012

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

- Mathematics
- 2013

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.

Identities of the left-symmetric Witt algebras

- MathematicsInt. J. Algebra Comput.
- 2016

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.