Results 261 to 270 of about 1,839,875 (302)
Some of the next articles are maybe not open access.
Lie Algebras and Lie Algebra Representations
, 2017In 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
An Introduction to Pre‐Lie Algebras
, 2021This is the note of my lectures that I will give at Expository Quantum Lecture Series 8: Quantization, Noncommutativity and Nonlinearity at the Institute for Mathematical Research (INSPEM) at Universiti Putra Malaysia (UPM) during January 18-22, 2016.
C. Bai
semanticscholar +1 more source
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
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
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
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
, 2014
In this paper, first we show that is a Hom–Lie algebra if and only if is an differential graded-commutative algebra. Then, we revisit representations of Hom–Lie algebras and show that there are a series of coboundary operators.
Y. Sheng, Zhen Xiong
semanticscholar +1 more source
In this paper, first we show that is a Hom–Lie algebra if and only if is an differential graded-commutative algebra. Then, we revisit representations of Hom–Lie algebras and show that there are a series of coboundary operators.
Y. Sheng, Zhen Xiong
semanticscholar +1 more source
Siberian Mathematical Journal, 1986
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +3 more sources
zbMATH Open Web Interface contents unavailable due to conflicting licenses.
openaire +3 more sources
Affine Lie Algebra Modules and Complete Lie Algebras
Algebra Colloquium, 2006In 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
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.
openaire +2 more sources
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.
openaire +2 more sources
Structure and Cohomology of 3-Lie Algebras Induced by Lie Algebras
, 2013The aim of this paper is to compare the structure and the cohomology spaces of Lie algebras and induced \(3\)-Lie algebras.
Joakim Arnlind +3 more
semanticscholar +1 more source