We construct a special class of fermionic Novikov superalgebras from linear functions. We show that they are Novikov superalgebras. Then we give a complete classification of them, among which there are some non-associative examples. This method leads to several new examples which have not been described in the literature.
Hom-Lie algebra (superalgebra) structure appeared naturally in -deformations, based on -derivations of Witt and Virasoro algebras (superalgebras). They are a twisted version of Lie algebras (superalgebras), obtained by deforming the Jacobi identity by a homomorphism. In this paper, we discuss the concept of -derivation, a representation theory, and provide a cohomology complex of Hom-Lie superalgebras. Moreover, we study central extensions. As application, we compute derivations and the second...
La première partie de cet article est une adaptation au cadre des super groupes d’un théorème dû à Cartier qui assure que les groupes formels sont lisses en caractéristique zéro. La seconde partie donne une description des super groupes de Lie dits “vraiment classiques” comme groupes d’automorphismes de super algèbres semi-simples associatives à involution, selon une méthode de Weil.
We show that a free graded commutative Banach algebra over a (purely odd) Banach space is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if is infinite-dimensional. Thus, a large amount of new examples of separable Banach-Grassmann algebras arise in addition to the only one example previously known due to A. Rogers.
We describe a collection of differential graded rings that categorify weight spaces of the positive half of the quantized universal enveloping algebra of the Lie superalgebra 𝔤𝔩(1|2).
We study Jordan (θ,θ)-superderivations and Jordan triple (θ,θ)-superderivations of superalgebras, using the theory of functional identities in superalgebras. As a consequence, we prove that if A = A₀ ⊕ A₁ is a prime superalgebra with deg(A₁) ≥ 9, then Jordan superderivations and Jordan triple superderivations of A are superderivations of A, and generalized Jordan superderivations and generalized Jordan triple superderivations of A are generalized superderivations of A.
Novikov superalgebras are related to quadratic conformal superalgebras which correspond to the Hamiltonian pairs and play a fundamental role in completely integrable systems. In this note we show that the Novikov superalgebras with and are of type and give a class of Novikov superalgebras of type with .
The category of group-graded modules over an abelian group is a monoidal category. For any bicharacter of this category becomes a braided monoidal category. We define the notion of a Lie algebra in this category generalizing the concepts of Lie super and Lie color algebras. Our Lie algebras have -ary multiplications between various graded components. They possess universal enveloping algebras that are Hopf algebras in the given category. Their biproducts with the group ring are noncommutative...
Nous généralisons un résultat de dualité dans les représentations coinduites établi par M. Duflo (dans [Du]) dans le cas des algèbres de Lie de dimension finie. La démonstration que nous en proposons utilise la superalgèbre des opérateurs différentiels sur le module coinduit ainsi que la correspondance, mise en évidence par J. Bernstein, entre -modules à droite et -modules à gauche. Elle n’est valable qu’en caractéristique zéro. Nous donnons aussi une interprétation de ce théorème en termes de...