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Project Euclid (Hosted at Cornell University Library) (196.854 recursos)
Journal of Generalized Lie Theory and Applications
Journal of Generalized Lie Theory and Applications
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...
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...
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.
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.
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.
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.
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.
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.
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.
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.