On the derivation algebra and the holomorph of a nilpotent algebra

1955 ◽  
Vol 0 (14) ◽  
pp. 0-0 ◽  
Author(s):  
Eugene Schenkman
Keyword(s):  
Nilpotent Algebra ◽  
Derivation Algebra

Derivation algebra of semi-direct sum of Lie algebras

2021 ◽  
pp. 2250063
Author(s):  
Mohammad Reza Alemi ◽  
Farshid Saeedi
Keyword(s):  
Lie Algebras ◽  
Arbitrary Field ◽  
Direct Sum ◽  
Derivation Algebra

Let [Formula: see text] and [Formula: see text] be two Lie algebras over an arbitrary field [Formula: see text], and let [Formula: see text] be the semidirect sum of [Formula: see text] by [Formula: see text]. In this paper, we give the structure of derivation algebra of [Formula: see text]; then as a consequence we illustrate the structure and dimension derivation algebra of Heisenberg Lie algebras.

scholarly journals The Derivation Algebra of Lie Algebra Der(Cq)∝Cq

2015 ◽  
Vol 05 (01) ◽  
pp. 1-7
Author(s):  
志龙 张
Keyword(s):  
Lie Algebra ◽  
Derivation Algebra

Derivations and Automorphism Group of Completed Witt Lie Algebra

2012 ◽  
Vol 19 (03) ◽  
pp. 581-590 ◽  
Author(s):  
Yongping Wu ◽  
Ying Xu ◽  
Lamei Yuan
Keyword(s):  
Finite Element ◽  
Automorphism Group ◽  
Lie Algebra ◽  
Cohomology Group ◽  
Locally Finite ◽  
Simple Lie Algebra ◽  
Derivation Algebra ◽  
First Cohomology Group

In this paper, a simple Lie algebra, referred to as the completed Witt Lie algebra, is introduced. Its derivation algebra and automorphism group are completely described. As a by-product, it is obtained that the first cohomology group of this Lie algebra with coefficients in its adjoint module is trivial. Furthermore, we completely determine the conjugate classes of this Lie algebra under its automorphism group, and also obtain that this Lie algebra does not contain any nonzero ad -locally finite element.

Double Derivations of n-Lie Superalgebras

2018 ◽  
Vol 25 (01) ◽  
pp. 161-180
Author(s):  
Bing Sun ◽  
Liangyun Chen ◽  
Xin Zhou
Keyword(s):  
Lie Superalgebra ◽  
Lie Superalgebras ◽  
General Linear ◽  
Base Field ◽  
Inner Derivation ◽  
Derivation Algebra ◽  
General Linear Lie Superalgebra

Let 𝔤 be an n-Lie superalgebra. We study the double derivation algebra [Formula: see text] and describe the relation between [Formula: see text] and the usual derivation Lie superalgebra Der(𝔤). We show that the set [Formula: see text] of all double derivations is a subalgebra of the general linear Lie superalgebra gl(𝔤) and the inner derivation algebra ad(𝔤) is an ideal of [Formula: see text]. We also show that if 𝔤 is a perfect n-Lie superalgebra with certain constraints on the base field, then the centralizer of ad(𝔤) in [Formula: see text] is trivial. Finally, we give that for every perfect n-Lie superalgebra 𝔤, the triple derivations of the derivation algebra Der(𝔤) are exactly the derivations of Der(𝔤).

scholarly journals Derivation algebra of direct sum of lie algebras

2019 ◽  
Vol 6 (1) ◽  
pp. 1624244
Author(s):  
Mohammad Reza Alemi ◽  
Farshid Saeedi ◽  
Hari M. Srivastava
Keyword(s):  
Lie Algebras ◽  
Direct Sum ◽  
Derivation Algebra

Derivations and Automorphism Group of Original Deformative Schrödinger-Virasoro Algebra

2015 ◽  
Vol 22 (03) ◽  
pp. 517-540 ◽  
Author(s):  
Qifen Jiang ◽  
Song Wang
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Direct Product ◽  
Virasoro Algebra ◽  
Witt Algebra ◽  
Tensor Density ◽  
Derivation Algebra

In this paper, we determine the derivation algebra and the automorphism group of the original deformative Schrödinger-Virasoro algebra, which is the semi-direct product Lie algebra of the Witt algebra and its tensor density module Ig(a,b).

Sign in / Sign up

Export Citation Format

Share Document