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Register a new userConformal $(si,t)$-Derivations on Lie conformal superalgebras
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In this paper, we focus on the $(si,t)$-derivation theory of Lie conformal superalgebras. Firstly, we study the fundamental properties of conformal $(si,t)$-derivations. Secondly, we mainly research the interiors of conformal $G$-derivations. Finally, we discuss the relationships between the conformal $(si,t)$-derivations and some generalized conformal derivations of Lie conformal superalgebras.
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We show that in the class of solvable Lie algebras there exist algebras which admit local derivations which are not ordinary derivation and also algebras for which every local derivation is a derivation. We found necessary and sufficient conditions under which any local derivation of solvable Lie algebras with abelian nilradical and one-dimensional complementary space is a derivation. Moreover, we prove that every local derivation on a finite-dimensional solvable Lie algebra with model nilradical and maximal dimension of complementary space is a derivation.
Suppose the ground field $mathbb{F}$ is an algebraically closed field of characteristic different from 2, 3. We determine the Betti numbers and make a decomposition of the associative superalgebra of the cohomology for the model filiform Lie superalgebra. We also describe the associative superalgebra structures of the (divided power) cohomology for some low-dimensional filiform Lie superalgebras.
We initiate a study on a range of new generalized derivations of finite-dimensional Lie algebras over an algebraically closed field of characteristic zero. This new generalization of derivations has an analogue in the theory of associative prime rings and unites many well-known generalized derivations that have already appeared extensively in the study of Lie algebras and other nonassociative algebras. After exploiting fundamental properties, we introduce and analyze their interiors, especially focusing on the rationality of the corresponding Hilbert series. Applying techniques in computational ideal theory we develop an approach to explicitly compute these new generalized derivations for the three-dimensional special linear Lie algebra over the complex field.
We classify finite irreducible conformal modules over a class of infinite Lie conformal algebras ${frak {B}}(p)$ of Block type, where $p$ is a nonzero complex number. In particular, we obtain that a finite irreducible conformal module over ${frak {B}}(p)$ may be a nontrivial extension of a finite conformal module over ${frak {Vir}}$ if $p=-1$, where ${frak {Vir}}$ is a Virasoro conformal subalgebra of ${frak {B}}(p)$. As a byproduct, we also obtain the classification of finite irreducible conformal modules over a series of finite Lie conformal algebras ${frak b}(n)$ for $nge1$.
Let $L$ be a Lie superalgebra over a field of characteristic different from $2,3$ and write $mathrm{ID}^{*}(L)$ for the Lie superalgebra consisting of superderivations mapping $L$ to $L^{2}$ and the central elements to zero. In this paper we first give an upper bound for the superdimension of $mathrm{ID}^{*}(L)$ by means of linear vector space decompositions. Then we characterize the $mathrm{ID}^{*}$-superderivation superalgebras for the nilpotent Lie superalgebras of class 2 and the model filiform Lie superalgebras by methods of block matrices.
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