arXiv subjects

Bruno Leonardo Macedo Ferreira

Publications and source records attributed to Bruno Leonardo Macedo Ferreira.

16 recordsLinked to original sources

arXiv2025

On the additivity of n-multiplicative isomorphisms, derivations, and related maps in axial algebras

In this paper, we demonstrate that several classes of functions, specifically n-multiplicative isomorphisms, derivations, elementary maps, and Jordan elementary maps on a class of algebras that includes Jordan algebras with idempotents, J(a)-axial algebras and M(a,b)-axial algebras, are additive under appropriate conditions, which may be referred to as Martindale-type conditions. Furthermore, we answer the question left open in the recent article titled "Multiplicative isomorphisms and derivations on axial algebra."

math.RA↗

arXiv2024

Exploring Functional Identities: From Division Rings to Matrix Algebras

In this paper, we tackle unresolved inquiries by Ferreira et al. \cite{bruno} in their recent publication, ``Functional Identity on Division Algebras". We delve into the intricate behavior of additive functions on matrix algebras over division rings through rigorous analysis and theorem-proving. Our findings offer valuable insights into the nature of these functions and their implications for algebraic structures.

math.RA↗

arXiv2024

Unraveling Functional Equations in Composition Algebra: Resolving Conjectures and Examining Implications

We address the conjectures left by the recent article by Ferreira et al. titled ``Commuting maps and identities with inverses on alternative division rings.'' We also present an example showing the necessity of the conditions of the results that answer the conjectures.

math.RA↗

arXiv2024

Transposed Poisson structures

To present a survey on known results from the theory of transposed Poisson algebras, as well as to establish new results on this subject, are the main aims of the present paper. Furthermore, a list of open questions for future research is given.

math.RA↗

arXiv2021

-Lie-Type maps on alternative -algebras

Let $A$ and $A'$ be two alternative $*$-algebras with identities 1_A and 1_A', respectively, and e_1 and e_2 = 1_A - e_1 nontrivial symmetric idempotents in A. In this paper we study the characterization of multiplicative *-Lie-type maps. As application, we get a result on alternative W*-algebras.

math.RA↗

arXiv2021

$\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras

A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson algebras was established. Some non-trivial transposed Poisson algebras with a certain Lie algebra (Witt algebra, algebra $\mathcal{W}(a,-1)$, thin Lie algebra and solvable Lie algebra with abelian nilpotent radical) were constructed. In particular, we constructed an example of the transposed Poisson algebra with associative and Lie parts isomorphic to the Laurent polynomials and the Witt algebra. On the other side, it was proven that there are no non-trivial transposed Poisson algebras with Lie algebra part isomorphic to a semisimple finite-dimensional algebra, a simple finite-dimensional superalgebra, the Virasoro algebra, $N=1$ and $N=2$ superconformal algebras, or a semisimple finite-dimensional $n$-Lie algebra.

math.RA↗

arXiv2021

Local and $2$-local derivations of simple $n$-ary algebras

In the present paper, we prove that every local and $2$-local derivation of the complex finite-dimensional simple Filippov algebra is a derivation. As a corollary we have the description of all local and $2$-local derivations of complex finite-dimensional semisimple Filippov algebras. All local derivations of the ternary Malcev algebra $M_8$ are described. It is the first example of a finite-dimensional simple algebra that admits pure local derivations, i.e. algebra admits a local derivation which is not a derivation.

math.RA↗

arXiv2021

$$-Lie-type maps on $C^$-algebras

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial symmetric projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $*$-Lie-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every complex scalar multiplication bijective unital multiplicative $*$-Lie-type map is $*$-isomorphism.

math.OA↗

arXiv2021

Additivity of $n$-Multiplicative Mappings of Gamma Rings

In this paper, we address the additivity of $n$-multiplicative isomorphisms and $n$-multiplicative derivations on Gamma rings. We proved that, if $\M$ is a $Γ$-ring satisfying the some conditions, then any $n$-multiplicative isomorphism $\left(φ, ϕ\right)$ of $\M$ onto an arbitrary gamma ring is additive.

math.RA↗

arXiv2021

Nonlinear $$-Jordan-type derivations on alternative $$-algebras

Let $A$ be an unital alternative $*$-algebra. Assume that $A$ contains a nontrivial symmetric idempotent element $e$ which satisfies $xA \cdot e = 0$ implies $x = 0$ and $xA \cdot (1_A - e) = 0$ implies $x = 0$. In this paper, it is shown that $Φ$ is a nonlinear $*$-Jordan-type derivation on A if and only if $Φ$ is an additive $*$-derivation. As application, we get a result on alternative $W^{*}$-algebras.

math.RA↗

arXiv2020

$$-Jordan-type maps on $C^{}$-algebras

Let $\mathfrak{A}$ and $\mathfrak{A}'$ be two $C^*$-algebras with identities $I_{\mathfrak{A}}$ and $I_{\mathfrak{A}'}$, respectively, and $P_1$ and $P_2 = I_{\mathfrak{A}} - P_1$ nontrivial projections in $\mathfrak{A}$. In this paper we study the characterization of multiplicative $*$-Jordan-type maps. In particular, if $\mathcal{M}$ is a factor von Neumann algebra then every bijective unital multiplicative $*$-Jordan-type maps are $*$-ring isomorphisms.

math.OA↗

arXiv2020

$$-Lie-Jordan-type maps on $C^{}$-algebras

Let A and A' be two Cstar-algebras with identities I_A and I_A', respectively, and P_1 and P_2 = I_A - P_1 nontrivial projections in A. In this paper we study the characterization of multiplicative star-Lie-Jordan-type maps, where the notion of these maps arise here. In particular, if M_A is a von Neumann algebra relative Cstar-algebra A without central summands of type I_1 then every bijective unital multiplicative star-Lie-Jordan-type maps are star-ring isomorphisms.

math.OA↗

arXiv2020

Commuting maps on alternative rings

Suppose $\mathfrak{R}$ is a $2$,$3$-torsion free unital alternative ring having an idempotent element $e_1$ $\left(e_2 = 1-e_1\right)$ which satisfies $x \mathfrak{R} \cdot e_i = \{0\} \rightarrow x = 0$ $\left(i = 1,2\right)$. In this paper, we aim to characterize the commuting maps. Let $φ$ be a commuting map of $\mathfrak{R}$ so it is shown that $φ(x) = zx + Ξ(x)$ for all $x \in \mathfrak{R}$, where $z \in \mathcal{Z}(\mathfrak{R})$ and $Ξ$ is an additive map from $\mathfrak{R}$ into $\mathcal{Z}(\mathfrak{R})$. As a consequence a characterization of anti-commuting maps is obtained and we provide as an application, a characterization of commuting maps on von Neumann algebras relative alternative $C^{*}$-algebra with no central summands of type $I_1$.

math.RA↗

arXiv2020

Lie maps on alternative rings preserving idempotents

Let $\Re$ and $\Re'$ unital $2$,$3$-torsion free alternative rings and $φ: \Re \rightarrow \Re'$ be a surjective Lie multiplicative map that preserves idempotents. Assume that $\Re$ has a nontrivial idempotents. Under certain assumptions on $\Re$, we prove that $φ$ is of the form $ψ+ τ$, where $ψ$ is either an isomorphism or the negative of an anti-isomorphism of $\Re$ onto $\Re'$ and $τ$ is an additive mapping of $\Re$ into the centre of $\Re'$ which maps commutators into zero.

math.RA↗

arXiv2020

Multiplicative Lie-type derivations on alternative rings

Let $\R$ be an alternative ring containing a nontrivial idempotent and $\D$ be a multiplicative Lie-type derivation from $\R$ into itself. Under certain assumptions on $\R$, we prove that $\D$ is almost additive. Let $p_n(x_1, x_2, \cdots, x_n)$ be the $(n-1)$-th commutator defined by $n$ indeterminates $x_1, \cdots, x_n$. If $\R$ is a unital alternative ring with a nontrivial idempotent and is $\{2,3,n-1,n-3\}$-torsion free, it is shown under certain condition of $\R$ and $\D$, that $\D=δ+τ$, where $δ$ is a derivation and $τ\colon\R\longrightarrow{\mathcal Z}(\R)$ such that $τ(p_n(a_1,\ldots,a_n))=0$ for all $a_1,\ldots,a_n\in\R$.

math.RA↗

arXiv2018

Generalized Jordan derivations of Incidence Algebras

For a given ring $\mathfrak{R}$ and a locally finite pre-ordered set $(X, \leq)$, consider $I(X, \mathfrak{R})$ to be the incidence algebra of $X$ over $\mathfrak{R}$. Motivated by a Xiao's result which states that every Jordan derivation of $I(X,\mathfrak{R})$ is a derivation in the case $\mathfrak{R}$ is $2$-torsion free, one proves that each generalized Jordan derivation of $I(X,\mathfrak{R})$ is a generalized derivation provided $\mathfrak{R}$ is $2$-torsion free, getting as a consequence the above mentioned result.

math.OA↗