Quadratic Lie conformal superalgebras related to Novikov superalgebras
نویسندگان
چکیده
We study quadratic Lie conformal superalgebras associated with Novikov superalgebras. For every superalgebra $(V,\circ)$, we construct an enveloping differential Poisson $U(V)$ a derivation $d$ such that $u\circ v=ud(v)$ and ${u,v}=u\circ v-(-1)^{|u||v|}v\circ u$ for $u,v\in V$. The latter means the commutator Gelfand–Dorfman of $V$ is special. Next, prove constructed on finite-dimensional special has finite faithful representation. This statement step towards solution following open problem: whether (super)algebra
منابع مشابه
Universally defined representations of Lie conformal superalgebras
We distinguish a class of irreducible finite representations of conformal Lie (super)algebras. These representations (called universally defined) are the simplest ones from the computational point of view: a universally defined representation of a conformal Lie (super)algebra L is completely determined by commutation relations of L and by the requirement of associative locality of generators. W...
متن کاملHom-Lie Superalgebras and Hom-Lie admissible Superalgebras
The purpose of this paper is to study Hom-Lie superalgebras, that is a superspace with a bracket for which the superJacobi identity is twisted by a homomorphism. This class is a particular case of Γ-graded quasi-Lie algebras introduced by Larsson and Silvestrov. In this paper, we characterize Hom-Lie admissible superalgebras and provide a construction theorem from which we derive a one paramete...
متن کاملGraded Lie Superalgebras, Supertrace Formula, and Orbit Lie Superalgebras
Let Γ be a countable abelian semigroup and A be a countable abelian group satisfying a certain finiteness condition. Suppose that a group G acts on a (Γ × A)-graded Lie superalgebra L = ⊕ (α,a)∈Γ×A L(α,a) by Lie superalgebra automorphisms preserving the (Γ × A)-gradation. In this paper, we show that the Euler-Poincaré principle yields the generalized denominator identity for L and derive a clos...
متن کاملDictionary on Lie Superalgebras
Foreword The main definitions and properties of Lie superalgebras are proposedà la façon de a short dictionary, the different items following the alphabetical order. The main topics deal with the structure of simple Lie superalgebras and their finite dimensional representations; rather naturally, a few pages are devoted to supersymmetry. This modest booklet has two ambitious goals: to be elemen...
متن کاملYangians of Lie Superalgebras
This thesis is concerned with extending some well-known results about the Yangians Y (glN) and Y (slN) to the case of super-Yangians. First we produce a new presentation of the Yangian Y (glm|n), using the Gauss decomposition of a matrix with non-commuting entries. Then, by writing the quantum Berezinian in terms of generators from the new presentation we prove that its coefficients generate th...
متن کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Noncommutative Geometry
سال: 2021
ISSN: ['1661-6960', '1661-6952']
DOI: https://doi.org/10.4171/jncg/445