Results 121 to 130 of about 297,060 (285)

Lie Algebra Prederivations and strongly nilpotent Lie Algebras [PDF]

Comm. in Algebra 30(7), 3157-3175 (2002), 2004
We study Lie algebra prederivations. A Lie algebra admitting a non-singular prederivation is nilpotent. We classify filiform Lie algebras admitting a non-singular prederivation but no non-singular derivation. We prove that any 4-step nilpotent Lie algebra admits a non-singular prederivation.
arxiv  

Counting integral points on symmetric varieties with applications to arithmetic statistics

Proceedings of the London Mathematical Society, Volume 130, Issue 4, April 2025.
Abstract In this article, we combine Bhargava's geometry‐of‐numbers methods with the dynamical point‐counting methods of Eskin–McMullen and Benoist–Oh to develop a new technique for counting integral points on symmetric varieties lying within fundamental domains for coregular representations.
Arul Shankar, Artane Siad, Ashvin A. Swaminathan   +2 more
wiley   +1 more source

Affine structures on filiform Lie algebras [PDF]

arXiv, 2001
In this note we prove that every non characteristically filiform Lie algebra is endowed with an affine structure.
arxiv  

Casimir invariants for quantized affine Lie algebras

Letters in Mathematical Physics, 1994
8 pages, LaTex file, UQMATH-93-04 (minor changes are made)
Gould, MD, Zhang, YZ
openaire   +4 more sources

Wakimoto Modules for Twisted Affine Lie Algebras [PDF]

Mathematical Research Letters, 2002
We construct Wakimoto modules for twisted affine Lie algebras, and interpret the construction in terms of vertex algebras and their twisted modules. Using the Wakimoto realization, we prove the Kac-Kazhdan conjecture on the characters of irreducible modules with generic critical highest weights in the twisted case.
openaire   +4 more sources

Irreducible Modules for Extended Affine Lie Algebras [PDF]

arXiv, 2010
We construct irreducible modules for twisted toroidal Lie algebras and extended affine Lie algebras. This is done by combining the representation theory of untwisted toroidal algebras with the technique of thin coverings of modules. We illustrate our method with examples of extended affine Lie algebras of Clifford type.
arxiv  

Frobenius structures and characters of affine Lie algebras [PDF]

Osaka Journal of Mathematics, 2017
35 pages. In this revision, Proposition 5.4 in the previous version is divided into 4 Propositions (from Proposition 5.4 to Proposition 5.7).
openaire   +4 more sources

Local charges in involution and hierarchies in integrable sigma-models

Journal of High Energy Physics, 2017
Integrable σ-models, such as the principal chiral model, ℤ T $$ {\mathbb{Z}}_T $$ -coset models for T ∈ ℤ ≥ 2 $$ T\in {\mathbb{Z}}_{\ge 2} $$ and their various integrable deformations, are examples of non-ultralocal integrable field theories described by
S. Lacroix, M. Magro, B. Vicedo
doaj   +1 more source

Time optimal problems on Lie groups and applications to quantum control

Communications in Analysis and Mechanics
In this paper we introduce a natural compactification of a left (right) invariant affine control system on a semi-simple Lie group $ G $ in which the control functions belong to the Lie algebra of a compact Lie subgroup $ K $ of $ G $ and we investigate ...
Velimir Jurdjevic
doaj   +1 more source

Unitary highest weight modules of locally affine Lie algebras [PDF]

arXiv, 2009
Locally affine Lie algebras are generalizations of affine Kac--Moody algebras with Cartan subalgebras of infinite rank whose root system is locally affine. In this note we study a class of representations of locally affine algebras generalizing integrable highest weight modules.
arxiv