نتایج جستجو برای: nilpotent lie algebra

تعداد نتایج: 111045  

Journal: :Communications in Mathematics 2023

We obtain inductive and enumerative formulas for the multiplicities of weights spin module Clifford algebra a Levi subalgebra in complex semisimple Lie algebra. Our involve only matrices tableaux, our techniques combine linear algebra, theory, combinatorics. Moreover, this suggests relationship with nilpotent orbits. The case special $\mathfrak{sl}(n,{\mathbb C})$ is emphasized.

2001
Rutwig Campoamor-Stursberg

We study a certain class of non-maximal rank contractions of the nilpotent Lie algebra gm and show that these contractions are completable Lie algebras. As a consequence a family of solvable complete Lie algebras of non-maximal rank is given in arbitrary dimension. . AMS Math. Subj. Class. 17B10, 17B30.

Journal: :Revista De La Real Academia De Ciencias Exactas Fisicas Y Naturales Serie A-matematicas 2021

A relation between $\frac{1}{2}$-derivations of Lie algebras and transposed Poisson was established. Some non-trivial with a certain algebra (Witt algebra, $\mathcal{W}(a,-1)$, thin solvable abelian nilpotent radical) were constructed. In particular, we constructed an example the associative parts isomorphic to Laurent polynomials Witt algebra. On other side, it proven that there are no part se...

2010
NICO VAN DEN HIJLIGENBERG YOURI KOTCHETKOV

For the Lie algebras L\(H(2)) and L\(W(2)), we study their infinitesimal deformations and the corresponding global ones. We show that, as in the case of L\{W(\)), each integrable infinitesimal deformation of L\(H(2)) and L1(W/(2)) can be represented by a 2-cocycle that defines a global deformation by means of a trivial extension. We also illustrate that all deformations of L\{H{2)) arise as res...

2001
Paola Cellini Paolo Papi PAOLA CELLINI PAOLO PAPI

We provide an explicit bijection between the ad-nilpotent ideals of a Borel subalgebra of a simple Lie algebra g and the orbits of Q̌/(h + 1)Q̌ under the Weyl group (Q̌ being the coroot lattice and h the Coxeter number of g). From this result we deduce in a uniform way a counting formula for the ad-nilpotent ideals.

2000
V. K. KHARCHENKO

We propose a notion of a quantum universal enveloping algebra for an arbitrary Lie algebra defined by generators and relations which is based on the quantum Lie operation concept. This enveloping algebra has a PBW basis that admits the Kashiwara crystalization. We describe all skew primitive elements of the quantum universal enveloping algebra for the classical nilpotent algebras of the infinit...

1999
MONICA NEVINS

The orbit method conjectures a close relationship between the set of irreducible unitary representations of a Lie group G, and admissible coadjoint orbits in the dual of the Lie algebra. We define admissibility for nilpotent coadjoint orbits of p-adic reductive Lie groups, and compute the set of admissible orbits for a range of examples. We find that for unitary, symplectic, orthogonal, general...

Journal: :Transformation Groups 2022

To each complex semisimple Lie algebra $$ \mathfrak{g} and regular element a ∈ reg, one associates Mishchenko–Fomenko subalgebra \mathcal{F} ⊆ ℂ[ ]. This amounts to completely integrable system on the Poisson variety , as such has bifurcation diagram Σa Spec( a). We prove that codimension in a) if reg is not nilpotent, it or two nilpotent. In nilpotent case, we show of possible codimensions be ...

1988
Matthew Grayson Robert Grossman

If a Lie algebra g can be generated by M of its elements E1, . . . , EM , and if any other Lie algebra generated by M other elements F1, . . . , FM is a homomorphic image of g under the map Ei → Fi, we say that it is the free Lie algebra on M generators. The free nilpotent Lie algebra gM,r on M generators of rank r is the quotient of the free Lie algebra by the ideal gr+1 generated as follows: ...

2008
TRACY L. PAYNE

We show that a left-invariant metric g on a nilpotent Lie group N is a soliton metric if and only if a matrix U and vector v associated the manifold (N, g) satisfy the matrix equation Uv = [1], where [1] is a vector with every entry a one. We associate a generalized Cartan matrix to the matrix U and use the theory of Kac-Moody algebras to analyze the solution spaces for such linear systems. We ...

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