Results 301 to 310 of about 1,737,526 (356)

Lie Algebras and Lie Algebra Representations

, 2017
In this chapter, we will introduce Lie algebras and Lie algebra representations, which provide a tractable linear construction that captures much of the behavior of Lie groups and Lie group representations.
P. Woit
semanticscholar   +2 more sources

-(bi)derivations and transposed Poisson algebra structures on Lie algebras

Linear and multilinear algebra, 2021
In the present paper, we introduce the notion of a δ-biderivation. First, we provide some properties of δ-biderivations and illustrate their applications.
Lamei Yuan, Q. Hua
semanticscholar   +1 more source

Polynomial Lie Algebras

Functional Analysis and Its Applications, 2002
Let \(P\) be an algebra of complex polynomials in \(\lambda_0, \ldots, \lambda_n\) and \(L_P\) the free left \(P\)-module with a basis \(1, l_0, \ldots, l_n\). Define the structure of a Lie algebra \(\mathfrak a(C,V)\) on \(L_P\) by setting \[ [l_i,l_j]=\sum c_{i,j}^k(\lambda)l_k,\quad [l_i,\lambda_q]=v_{i,q}(\lambda), \quad [\lambda_i,\lambda_j]=0, \]
Bukhshtaber, V. M., Leĭkin, D. V.
openaire   +2 more sources

Antinilpotent Lie Algebras

Mathematical Notes, 2005
A Lie algebra is said to be antinilpotent if any of its nilpotent subalgebras is abelian. The main motivation to consider the class of antinilpotent Lie algebras is the relation (first mentioned in [\textit{E. Dalmer}, J. Math. Phys. 40, No. 8, 4151--4156 (1999; Zbl 0966.17003)]) between antinilpotent Lie algebras and the problem of constructing ...
openaire   +2 more sources

M. Kontsevich’s graph complex and the Grothendieck–Teichmüller Lie algebra

, 2010
We show that the zeroth cohomology of M. Kontsevich’s graph complex is isomorphic to the Grothendieck–Teichmüller Lie algebra $$\mathfrak {{grt}}_1$$grt1. The map is explicitly described. This result has applications to deformation quantization and Duflo
T. Willwacher
semanticscholar   +1 more source

n-Lie algebras

Siberian Mathematical Journal, 1986
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire   +3 more sources

Affine Lie Algebra Modules and Complete Lie Algebras

Algebra Colloquium, 2006
In this paper, we first construct some new infinite dimensional Lie algebras by using the integrable modules of affine Lie algebras. Then we prove that these new Lie algebras are complete. We also prove that the generalized Borel subalgebras and the generalized parabolic subalgebras of these Lie algebras are complete.
Gao, Yongcun, Meng, Daoji
openaire   +2 more sources

LOCAL LIE ALGEBRAS

Russian Mathematical Surveys, 1976
In this article we investigate the structure of local Lie algebras with a one-dimensional fibre. We show that all such Lie algebras are essentially exhausted by the classical examples of the Hamiltonian and contact Poisson bracket algebras. We give some examples, unsolved problems, and applications of Lie superalgebras.
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Algebra, Lie Group and Lie Algebra

2010
Geometry, algebra, and analysis are usually called the three main branches of mathematics. This chapter introduces some fundamental results in algebra that are mostly useful in systems and control. In section 4.1 some basic concepts of group and three homomorphism theorems are discussed. Ring and algebra are introduced briefly in section 4.2. As a tool,
Daizhan Cheng, Xiaoming Hu, Tielong Shen
openaire   +1 more source