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A class of fermionic Novikov superalgebras which is a class of Novikov superalgebras

Huibin Chen, Shaoqiang Deng (2018)

Czechoslovak Mathematical Journal

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.

Cohomology of Hom-Lie superalgebras and q -deformed Witt superalgebra

Faouzi Ammar, Abdenacer Makhlouf, Nejib Saadaoui (2013)

Czechoslovak Mathematical Journal

Hom-Lie algebra (superalgebra) structure appeared naturally in q -deformations, based on σ -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 α k -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...

Conservative algebras and superalgebras: a survey

Yury Popov (2020)

Communications in Mathematics

We give a survey of results obtained on the class of conservative algebras and superalgebras, as well as on their important subvarieties, such as terminal algebras.

Description de certains super groupes classiques

Caroline Gruson (1994)

Annales de l'institut Fourier

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.

General construction of Banach-Grassmann algebras

Vladimir G. Pestov (1992)

Atti della Accademia Nazionale dei Lincei. Classe di Scienze Fisiche, Matematiche e Naturali. Rendiconti Lincei. Matematica e Applicazioni

We show that a free graded commutative Banach algebra over a (purely odd) Banach space E is a Banach-Grassmann algebra in the sense of Jadczyk and Pilch if and only if E 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.

How to categorify one-half of quantum 𝔤𝔩(1|2)

Mikhail Khovanov (2014)

Banach Center Publications

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).

Jordan superderivations and Jordan triple superderivations of superalgebras

He Yuan, Liangyun Chen (2016)

Colloquium Mathematicae

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 with A 0 = A 1 A 1

Fuhai Zhu, Zhiqi Chen (2010)

Czechoslovak Mathematical Journal

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 A 0 = A 1 A 1 and dim A 1 = 2 are of type N and give a class of Novikov superalgebras of type S with A 0 = A 1 A 1 .

On Lie algebras in braided categories

Bodo Pareigis (1997)

Banach Center Publications

The category of group-graded modules over an abelian group G is a monoidal category. For any bicharacter of G 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 n -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...

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