Mostrando recursos 1 - 10 de 10

  1. On Derivations of Some Classes of Leibniz Algebras

    Rakhimov, Isamiddin S.; Al-Nashri, Al-Hossain
    In this paper, we describe the derivations of complex $n$-dimensional naturally graded filiform Leibniz algebras $\mathrm{NGF_1}$, $\mathrm{NGF_2}$, and $\mathrm{NGF_3}$.We show that the dimension of the derivation algebras of $\mathrm{NGF_1}$ and $\mathrm{NGF_2}$ equals $n+1$ and $n+2$, respectively, while the dimension of the derivation algebra of $\mathrm{NGF_3}$ is equal to $2n−1$. The second part of the paper deals with the description of the derivations of complex $n$-dimensional filiform non Lie Leibniz algebras, obtained from naturally graded non Lie filiform Leibniz algebras. It is well known that this class is split into two classes denoted by $\mathrm{FLb}_n$ and $\mathrm{SLb}_n$. Here we found that for $L ∈ \mathrm{FLb}_n$, we...

  2. On Derivations of Some Classes of Leibniz Algebras

    Rakhimov, Isamiddin S.; Al-Nashri, Al-Hossain
    In this paper, we describe the derivations of complex $n$-dimensional naturally graded filiform Leibniz algebras $\mathrm{NGF_1}$, $\mathrm{NGF_2}$, and $\mathrm{NGF_3}$.We show that the dimension of the derivation algebras of $\mathrm{NGF_1}$ and $\mathrm{NGF_2}$ equals $n+1$ and $n+2$, respectively, while the dimension of the derivation algebra of $\mathrm{NGF_3}$ is equal to $2n−1$. The second part of the paper deals with the description of the derivations of complex $n$-dimensional filiform non Lie Leibniz algebras, obtained from naturally graded non Lie filiform Leibniz algebras. It is well known that this class is split into two classes denoted by $\mathrm{FLb}_n$ and $\mathrm{SLb}_n$. Here we found that for $L ∈ \mathrm{FLb}_n$, we...

  3. Quantizations of Group Actions

    Huru, Hilja L.; Lychagin, Valentin V.
    We describe quantizations on monoidal categories of modules over finite groups. Those are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over $S_3$ and $A_4$ we give explicit forms for all quantizations.

  4. Quantizations of Group Actions

    Huru, Hilja L.; Lychagin, Valentin V.
    We describe quantizations on monoidal categories of modules over finite groups. Those are given by quantizers which are elements of a group algebra. Over the complex numbers we find these explicitly. For modules over $S_3$ and $A_4$ we give explicit forms for all quantizations.

  5. Solvable and Nilpotent Radicals of the Fuzzy Lie Algebras

    Ferreira, J. C. da Motta; Marietto, M. G. Bruno
    In this paper, we apply the concepts of fuzzy sets to Lie algebras in order to introduce and to study the notions of solvable and nilpotent fuzzy radicals. We present conditions to prove the existence and uniqueness of such radicals.

  6. Solvable and Nilpotent Radicals of the Fuzzy Lie Algebras

    Ferreira, J. C. da Motta; Marietto, M. G. Bruno
    In this paper, we apply the concepts of fuzzy sets to Lie algebras in order to introduce and to study the notions of solvable and nilpotent fuzzy radicals. We present conditions to prove the existence and uniqueness of such radicals.

  7. Contractions of 3-Dimensional Representations of the Lie Algebra $\mathfrak{sl}(2)$

    Smotlacha, Jan; Chadzitaskos, Goce
    A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the $\mathbb{Z}_3$-grading of the $\mathfrak{sl}(2)$ Lie algebra.

  8. Contractions of 3-Dimensional Representations of the Lie Algebra $\mathfrak{sl}(2)$

    Smotlacha, Jan; Chadzitaskos, Goce
    A theory of grading preserving contractions of representations of Lie algebras has been developed. In this theory, grading of the given Lie algebra is characterized by two sets of parameters satisfying a derived set of equations. Here we introduce a list of resulting 3-dimensional representations for the $\mathbb{Z}_3$-grading of the $\mathfrak{sl}(2)$ Lie algebra.

  9. Automorphism Groups of Cayley-Dickson Loops

    Kirshtein, Jenya
    The Cayley-Dickson $Q_n$ loop is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, and sedenions).We discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian, and describe the structure of their automorphism groups.

  10. Automorphism Groups of Cayley-Dickson Loops

    Kirshtein, Jenya
    The Cayley-Dickson $Q_n$ loop is the multiplicative closure of basic elements of the algebra constructed by n applications of the Cayley-Dickson doubling process (the first few examples of such algebras are real numbers, complex numbers, quaternions, octonions, and sedenions).We discuss properties of the Cayley-Dickson loops, show that these loops are Hamiltonian, and describe the structure of their automorphism groups.

Aviso de cookies: Usamos cookies propias y de terceros para mejorar nuestros servicios, para análisis estadístico y para mostrarle publicidad. Si continua navegando consideramos que acepta su uso en los términos establecidos en la Política de cookies.