## 4 Citations

Lie nilpotent Novikov algebras and Lie solvable Leavitt path algebras

- Mathematics
- 2020

In this paper, we first study properties of the lower central chains for Novikov algebras. Then we show that for every Lie nilpotent Novikov algebra~$\mathcal{N}$, the ideal of~$\mathcal{N}$…

On a conjecture about solvability of symmetric Poisson algebras

- MathematicsBulletin of the London Mathematical Society
- 2021

For a Lie algebra L , let S(L) denote the symmetric Poisson algebra and s(L) the truncated symmetric Poisson algebra of L . In characteristic p≠2 , the conditions under which these Poisson algebras…

Products of commutator ideals of some Lie-admissible algebras

- Mathematics
- 2022

. In this article, we mainly study the products of commutator ideals of Lie-admissible algebras such as Novikov algebras, bicommutative algebras, and assosymmetric algebras. More precisely, we ﬁrst…

Scale for codimension growth of Poisson PI-algebras

- Mathematics
- 2021

A.Regev proved that the codimension growth of an associative PI-algebra is at most exponential. The author established a scale for the codimension growth of Lie PI-algebras, which includes a series…

## References

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PI-Algebras Generated by Nilpotent Elements of Bounded Index

- Mathematics
- 1997

Abstract Let R be an associative algebra over a field F of positive characteristic p . We address the following problem: if R is generated by nilpotent elements with bounded index, under what…

Lie Solvable Group Rings

- MathematicsCanadian Journal of Mathematics
- 1973

Let K[G] denote the group ring of G over the field K. One of the interesting problems which arises in the study of such rings is to find precisely when they satisfy polynomial identities. This has…

Poisson PI algebras

- Mathematics
- 2007

We study Poisson algebras satisfying polynomial identities. In particular, such algebras satisfy "customary"' identities (Farkas, 1998, 1999) Our main result is that the growth of the corresponding…

Poisson identities of enveloping algebras

- Mathematics
- 2006

Abstract.Let L be a restricted Lie algebra. The symmetric algebra Sp(L) of the restricted enveloping algebra u(L) has the structure of a Poisson algebra. We give necessary and sufficient conditions…

Radical Rings with Soluble Adjoint Groups

- Mathematics
- 2002

Abstract An associative ring R , not necessarily with an identity, is called radical if it coincides with its Jacobson radical, which means that the set of all elements of R forms a group denoted by…

Poisson polynomial identities II

- Mathematics
- 1998

Abstract. We study Poisson polynomial identities for the symmetric Poisson algebra of a Lie algebra and for the graded Poisson algebra associated to a ring of differential operators. Connections are…

Lie structure of smash products

- Mathematics
- 2017

We investigate the conditions under which the smash product of an (ordinary or restricted) enveloping algebra and a group algebra is Lie solvable or Lie nilpotent.