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.

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).

scholarly journals The Classification, Automorphism Group, and Derivation Algebra of the Loop Algebra Related to the Nappi–Witten Lie Algebra

2021 ◽  
Vol 2021 ◽  
pp. 1-14
Author(s):  
Xue Chen
Keyword(s):  
Automorphism Group ◽  
Lie Algebra ◽  
Loop Algebra ◽  
Isomorphism Classes ◽  
Derivation Algebra

Set L ≔ H 4 ⊗ ℂ R , R ≔ ℂ t ± 1 , and S ≔ ℂ t ± 1 / m m ∈ ℤ + . Then, L is called the loop Nappi–Witten Lie algebra. R -isomorphism classes of S / R forms of L are classified. The automorphism group and the derivation algebra of L are also characterized.

Outer Derivations and Classical-Albert-Zassenhaus lie Algebras

1984 ◽  
Vol 36 (6) ◽  
pp. 961-972 ◽  
Author(s):  
David J. Winter
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Maximal Torus ◽  
Cartan Subalgebra ◽  
One Dimensional ◽  
Derivation Algebra ◽  
Image Position

This paper is concerned with the structure of the derivation algebra Der L of the Lie algebra L with split Cartan subalgebra H. The Fitting decompositionof Der L with respect to ad ad H leads to a decompositionwhereThis decomposition is studied in detail in Section 2, where the centralizer of ad L∞ in D0(H) is shown to bewhich is Hom(L/L2, Center L) when H is Abelian. When the root-spaces La (a nonzero) are one-dimensional, this leads to the decomposition of Der L aswhere T is any maximal torus of D0(H).

On Reductive Lie Admissible Algebras

1971 ◽  
Vol 23 (2) ◽  
pp. 325-331 ◽  
Author(s):  
Arthur A. Sagle
Keyword(s):  
Vector Space ◽  
Lie Algebra ◽  
Associative Algebra ◽  
Commutative Algebra ◽  
Jacobi Identity ◽  
Direct Sum ◽  
Derivation Algebra ◽  
Image Position

A Lie admissible algebra is a non-associative algebra A such that A− is a Lie algebra where A− denotes the anti-commutative algebra with vector space A and with commutation [X, Y] = XY – YX as multiplication; see [1; 2; 5]. Next let L−(X): A− → A−: Y → [X, Y] and H = {L−(X): X ∊ A−}; then, since A− is a Lie algebra, we see that H is contained in the derivation algebra of A− and consequently the direct sum g = A − ⊕ H can be naturally made into a Lie algebra with multiplication [PQ] given by: P = X + L−(U), Q = Y + L−(V) ∊ g, thenand note that for any P, [PP] = 0 so that [PQ] = −[QP] and the Jacobi identity for g follows from the fact that A− is Lie.

On the Derivation Algebras of Lie Algebras

1961 ◽  
Vol 13 ◽  
pp. 201-216 ◽  
Author(s):  
Shigeaki Tôgô
Keyword(s):  
Lie Algebra ◽  
Lie Algebras ◽  
Intimate Connection ◽  
Derivation Algebra ◽  
Algebra Over A Field

LetLbe a Lie algebra over a field of characteristic 0 and letD(L)be the derivation algebra ofL, that is, the Lie algebra of all derivations ofL. Then it is natural to ask the following questions: What is the structure ofD(L)?What are the relations of the structures ofD(L)andL? It is the main purpose of this paper to present some results onD(L)as the answers to these questions in simple cases.Concerning the questions above, we give an example showing that there exist non-isomorphic Lie algebras whose derivation algebras are isomorphic (Example 3 in § 5). Therefore the structure of a Lie algebraLis not completely determined by the structure ofD(L). However, there is still some intimate connection between the structure ofD(L)and that ofL.

On the basis-conjugating automorphism groups of free groups and free metabelian groups

2014 ◽  
Vol 158 (1) ◽  
pp. 83-109 ◽  
Author(s):  
TAKAO SATOH
Keyword(s):  
Lie Algebra ◽  
Automorphism Groups ◽  
Free Groups ◽  
Metabelian Groups ◽  
Derivation Algebra ◽  
Trace Maps

AbstractIn this paper we study the images of the Johnson homomorphisms of the basis-conjugating automorphism groups of free groups and free metabelian groups. In particular, we show that the Johnson image is contained in a certain proper Lie subalgebra $\mathfrak{p}$Mn of the derivation algebra of the Chen Lie algebra. Furthermore, we completely determine the Johnson images, and give the abelianisation of $\mathfrak{p}$Mn as a Lie algebra by using Morita's trace maps.

The Even Part of Finite-Dimensional Modular Lie Superalgebra Γ

2021 ◽  
Vol 28 (03) ◽  
pp. 479-496
Author(s):  
Yusi Fan ◽  
Xiaoning Xu ◽  
Liangyun Chen
Keyword(s):  
Lie Algebra ◽  
Lie Superalgebra ◽  
Base Field ◽  
Modular Lie Superalgebra ◽  
Derivation Algebra ◽  
Finite Dimensional ◽  
Generator Sets

Let [Formula: see text] be the underlying base field of characteristic [Formula: see text] and denote by [Formula: see text] the even part of the finite-dimensional Lie superalgebra [Formula: see text]. We give the generator sets of the Lie algebra [Formula: see text]. Using certain properties of the canonical tori of [Formula: see text], we describe explicitly the derivation algebra of [Formula: see text].

scholarly journals Biderivations of the higher rank Witt algebra without anti-symmetric condition

2018 ◽  
Vol 16 (1) ◽  
pp. 447-452 ◽  
Author(s):  
Xiaomin Tang ◽  
Yu Yang
Keyword(s):  
Lie Algebra ◽  
Laurent Polynomial ◽  
Low Rank ◽  
Witt Algebra ◽  
Polynomial Algebras ◽  
Derivation Algebra ◽  
Higher Rank

AbstractThe Witt algebra 𝔚d of rank d(≥ 1) is the derivation algebra of Laurent polynomial algebras in d commuting variables. In this paper, all biderivations of 𝔚d without anti-symmetric condition are determined. As an applications, commutative post-Lie algebra structures on 𝔚d are obtained. Our conclusions recover and generalize results in the related papers on low rank or anti-symmetric cases.

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