Results 71 to 80 of about 2,755,034 (162)

Representations up to homotopy of Lie algebroids [PDF]

, 2017
We introduce and study the notion of representation up to homotopy of a Lie algebroid, paying special attention to examples. We use representations up to homotopy to define the adjoint representation of a Lie algebroid and show that the resulting ...
Abad, Camilo Arias, Crainic, Marius
core  

An Introduction to Lie Algebra [PDF]

, 2017
An (associative) algebra is a vector space over a field equipped with an associative, bilinear multiplication. By use of a new bilinear operation, any associative algebra morphs into a nonassociative abstract Lie algebra, where the new product in terms ...
Talley, Amanda Renee
core   +1 more source

Invariant Adjoint Tensors of the Classical Groups [PDF]

arXiv, 2015
For $\mathfrak{g}$ a simple Lie algebra and $G$ its adjoint group, the Chevalley map and work of Coxeter gives a concrete description of the algebra of $G$-invariant polynomials on $\mathfrak{g}$ in terms of traces over various representations. Here we provide an extension of this description to $G$-invariant tensors on $\mathfrak{g}$, although ...
arxiv  

Intrinsic construction of invariant functions on simple Lie algebras [PDF]

arXiv, 2013
An algorithm for constructing primitive adjoint-invariant functions on a complex simple Lie algebra is presented. The construction is intrinsic in the sense that it does not resort to any representation. A primitive invariant function on the whole Lie algebra is obtained by lifting a coordinate function on a Kostant slice of the Lie algebra.
arxiv  

A remarkable contraction of semisimple Lie algebras [PDF]

arXiv, 2011
Recently, E.Feigin introduced a very interesting contraction $\mathfrak q$ of a semisimple Lie algebra $\mathfrak g$ (see arXiv:1007.0646 and arXiv:1101.1898). We prove that these non-reductive Lie algebras retain good invariant-theoretic properties of $\mathfrak g$. For instance, the algebras of invariants of both adjoint and coadjoint representations
arxiv  

Graded multiplicities in the exterior algebra of the little adjoint module [PDF]

arXiv, 2018
As a first application of the double affine Hecke algebra with unequal parameters on Weyl orbits to representation theory of semisimple Lie algebras, we find the graded multiplicities of the trivial module and of the little adjoint module in the exterior algebra of the little adjoint module of a simple Lie algebra $\,\mathfrak{g}\,$ with a non-simply ...
arxiv  

A bialgebra theory of post-Lie algebras via Manin triples and generalized Hessian Lie groups [PDF]

arXiv
We develop a bialgebra theory of post-Lie algebras that can be characterized by Manin triples of post-Lie algebras associated to a bilinear form satisfying certain invariant conditions. In the absence of dual representations for adjoint representations of post-Lie algebras, we utilize the geometric interpretation of post-Lie algebras to find the ...
arxiv  

Sur la structure transverse à une orbite nilpotente adjointe [PDF]

arXiv, 2003
We are interested in Poisson structures transverse to nilpotent adjoint orbits in a complex semi-simple Lie algebra, and we study their polynomial nature, introduced by R.Cushman and M.Roberts. Furthermore, in the case of sl(n), we construct some families of nilpotent orbits with quadratic transverse structures.
arxiv  

A Jordan Algebra of a Mal’tsev Algebra

Journal of Mathematical Sciences, 2023
A. Golubkov
semanticscholar   +1 more source

Optimal system and dynamics of optical soliton solutions for the Schamel KdV equation. [PDF]

Sci Rep, 2023
Hussain A, Chahlaoui Y, Usman M, Zaman FD, Park C.   +4 more
europepmc   +1 more source