Lie solvable enveloping algebras of characteristic two

Siciliano, Salvatore; Usefi, Hamid

doi:10.1016/j.jalgebra.2013.02.016

Cited by 13 publications

(11 citation statements)

References 29 publications

Supporting

Mentioning

Contrasting

Unclassified

Order By: Relevance

“…It is worth mentioning that similar problems also arise in the setting of ordinary and restricted enveloping algebras (see, for example, [12,15]). In particular, for an arbitrary Lie algebra L, the combination of Theorem 1.4 with [15, Corollary 6.2] yields that S(L) is solvable if and only if the universal enveloping algebra of L is Lie solvable.…”

Section: Introductionmentioning

confidence: 95%

On a conjecture about solvability of symmetric Poisson algebras

Siciliano

Usefi

2021

Bull. London Math. Soc.

Self Cite

View full text Add to dashboard Cite

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 are solvable were established by Monteiro Alves and Petrogradsky in (J. Algebra 488 (2017) 244-281). The characterization in the harder case p = 2 was left as an open problem and a related conjecture formulated. In this paper, we prove a corrected version of that conjecture, which thereby completes the classification.

show abstract

Section: Introductionmentioning

confidence: 95%

On a conjecture about solvability of symmetric Poisson algebras

Siciliano

Usefi

2021

Bull. London Math. Soc.

Self Cite

View full text Add to dashboard Cite

show abstract

“…Example 3.6 ( [33]). Let F be a field of characteristic 2 containing two elements α, β such that the following condition holds: If λ 1 , λ 2 , λ 3 are in F and λ 2 1 + λ 2 2 α + λ 2 3 β = 0 then λ 1 = λ 2 = λ 3 = 0.…”

Section: The Lie Structure Of Restricted Enveloping Algebrasmentioning

confidence: 99%

Lie Properties of Restricted Enveloping Algebras

Siciliano¹,

Usefi²

2015

Contemporary Mathematics

Self Cite

View full text Add to dashboard Cite

To Professor Helmut Strade on the occasion of his 70 th birthday.Abstract. Let L be a restricted Lie algebra over a field of positive characteristic. We survey the known results about the Lie structure of the restricted enveloping algebra u(L) of L. Related results about the structure of the group of units and the symmetric and skew-symmetric elements of u(L) are also discussed. Moreover, a new theorem about an upper bound for the Lie nilpotency class of u(L) is proved.

show abstract

“…This result has been used numerously and proven to be very useful (see e.g. [1,9,13,14]). The primary goal of this paper is to prove a similar statement for Poisson algebras.…”

Section: Introductionmentioning

confidence: 99%

Solvability of Poisson algebras

Siciliano¹,

Usefi²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Let P be a Poisson algebra with a Lie bracket {, } over a field F of characteristic p ≥ 0. In this paper, the Lie structure of P is investigated. In particular, if P is solvable with respect to its Lie bracket, then we prove that the Poisson ideal J of P generated by all elements {{{x1, x2}, {x3, x4}}, x5} with x1, . . . , x5 ∈ P is associative nilpotent of index bounded by a function of the derived length of P . We use this result to further prove that if P is solvable and p = 2, then the Poisson ideal {P, P }P is nil.

show abstract

Lie solvable enveloping algebras of characteristic two

Cited by 13 publications

References 29 publications

On a conjecture about solvability of symmetric Poisson algebras

On a conjecture about solvability of symmetric Poisson algebras

Lie Properties of Restricted Enveloping Algebras

Solvability of Poisson algebras

Contact Info

Product

Resources

About