Odd-quadratic Leibniz superalgebras
-
Saïd Benayadi
and
Fahmi Mhamdi
Abstract
An odd-quadratic Leibniz superalgebra is a (left or right) Leibniz superalgebra with an odd, supersymmetric, non-degenerate and invariant bilinear form. In this paper, we prove that a left (resp. right) Leibniz superalgebra that carries this structure is symmetric (meaning that it is simultaneously a left and a right Leibniz superalgebra). Moreover, we show that any non-abelian (left or right) Leibniz superalgebra does not possess simultaneously a quadratic and an odd-quadratic structure. Further, we obtain an inductive description of odd-quadratic Leibniz superalgebras using the procedure of generalized odd double extension and we reduce the study of this class of Leibniz superalgebras to that of odd-quadratic Lie superalgebras. Finally, several non-trivial examples of odd-quadratic Leibniz superalgebras are included.
Acknowledgements
The authors are very grateful to the SMT for its organization of the 23rd conference March 19–22, 2018, in Tabarka, its kind invitation and hospitality.
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© 2019 Walter de Gruyter GmbH, Berlin/Boston
Articles in the same Issue
- Frontmatter
- 23rd Meeting of the Tunisian Mathematical Society (March 2018, Tabarka, Tunisia)
- Odd-quadratic Leibniz superalgebras
- Construction and stability of type I blowup solutions for non-variational semilinear parabolic systems
- Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces
- A virtual element method for a biharmonic Steklov eigenvalue problem
- Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem
- Dynamics of an ecological system
- Hilbert space valued Gabor frames in weighted amalgam spaces
- Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one
- A weighted inequality for potential type operators
- W-semisymmetric generalized Sasakian-space-forms
- Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space
- Existence of positive solutions for a Neumann boundary value problem on the half-line via coincidence degree
- Multi-norm structure based on enveloping 𝐶∗-algebras
- Multiplicative convolution of real asymmetric and real anti-symmetric matrices
Articles in the same Issue
- Frontmatter
- 23rd Meeting of the Tunisian Mathematical Society (March 2018, Tabarka, Tunisia)
- Odd-quadratic Leibniz superalgebras
- Construction and stability of type I blowup solutions for non-variational semilinear parabolic systems
- Operator Popoviciu’s inequality for superquadratic and convex functions of selfadjoint operators in Hilbert spaces
- A virtual element method for a biharmonic Steklov eigenvalue problem
- Convergence analysis of an inertial accelerated iterative algorithm for solving split variational inequality problem
- Dynamics of an ecological system
- Hilbert space valued Gabor frames in weighted amalgam spaces
- Laguerre–Freud equations associated with the D-Laguerre–Hahn forms of class one
- A weighted inequality for potential type operators
- W-semisymmetric generalized Sasakian-space-forms
- Proximal point algorithm involving fixed point of nonexpansive mapping in 𝑝-uniformly convex metric space
- Existence of positive solutions for a Neumann boundary value problem on the half-line via coincidence degree
- Multi-norm structure based on enveloping 𝐶∗-algebras
- Multiplicative convolution of real asymmetric and real anti-symmetric matrices
