Semisimple Lie algebras
On I null lie algebras
... complex Lie algebras for which the Koszul 3-form is zero, and prove that it contains all quotients of Borel subalgebras, or of their nilradicals, of finite dimensional complex semisimple Lie ...
22
Drinfel’d doubles and Shapovalov determinants
... enveloping algebras of semisimple Lie algebras the Weyl groupoid is nothing but the Weyl group of the Lie ...all algebras U (χ) with finite root ...complex semisimple ...
40
Generalized Serre relations for Lie algebras associated with positive unit forms
... Every semisimple Lie algebra defines a root system on the dual space of a Cartan subalgebra and a Cartan matrix, which expresses the dual of the Killing form on a root ...Complex Semisimple ...
14
On the structure of split involutive Hom Lie color algebras
... [α] 6= [β]. In Section 4, we show that under certain conditions, in the case of L being of maximal length, the simplicity of the algebra is characterized and it is shown that L is the direct sum of the family of its ...
17
$T^*$ extensions and abelian extensions of hom Lie color algebras
... hom- Lie color algebra, showing that the infinitesimal deformation generated by a hom- Nijenhuis operator is ...quadratic Lie color algebra L over an algebraically closed field of characteristic not 2 is ...
20
Álgebras de Lie solubles de baja dimensión
... de Lie de dimensi ´on finita g se descompone como un producto semidirecto de su ideal maximal soluble rad(g) y un ´algebra de Lie ...de Lie de dimensi ´on finita y, de alguna manera, justifica la b ...
40
La cohomología de Hochschild de álgebras de cuerdas y su estructura de álgebra de Gerstenhaber
... ´ algebras que son de este tipo se les puede asociar un carcaj con relaciones, lo que permite obtener informaci´ on sobre los grupos HH n (A, A), que de ahora en m´ as ser´ an notados HH n (A), a partir de datos ...
121
Joint spectrum for quasi solvable Lie algebras of operators
... In this section we extend the joint spectrum which we have defined from complex solvable finite dhnensional Lie algebras of operators to quasi-solvable Lie algebras of operators. As we have ...
9
On semisimple Hopf algebras with few representations of dimension greater than one
... some semisimple Hopf algebras, Contemp. Math. 483, Algebras, representations and applications, A conference in honour of Ivan Shestakov’s 60th birthday, August 26–September 1, 2007, Maresias, ...
15
A historical review of the classifications of Lie algebras
... semi-simple Lie algebras was completely solved by the well-known Cartan Theorem: any semi-simple complex or real Lie algebra can be decomposed into a direct sum of ideals which are simple subalgebras ...
25
On generalized Jordan prederivations and generalized prederivations of Lie color algebras
... Lie algebras and Lie superalgebras play important roles in many mathematical and physical subjects, ...of Lie theory corresponds to the study of symmetries into ...of Lie ...
13
Classification of real solvable Lie algebras whose simply connected Lie groups have only zero or maximal dimensional coadjoint orbits
... n-dimensional Lie algebras are MD-algebras, and moreover, they can be listed ...Diamond Lie algebra is the 3-dimensional Heisenberg Lie algebra which is non commutative and ...
25
On the Betti numbers of filiform Lie algebras over fields of characteristic two
... Lie algebras of Vergne type are Lie algebras of maximal class, in the sense that they have maximal ...Infinite Lie algebras of maximal class over fields of characteristic two ...
12
Lie $n$ multiplicative mappings on triangular $n$ matrix rings
... Proof. We shall only prove the first item because the demonstrations of the others are similar. It is important to note that if ϕ is Lie 2-multiplicative mapping (i.e., Lie multiplicative mapping), then ϕ ...
12
A classification of solvable quadratic and odd quadratic Lie superalgebras in low dimensions
... a Lie algebra g and its dual space g ∗ can be comprehended that the Lie algebra g is “glued” by g ∗ ...quadratic Lie algebra (h, ...quadratic Lie superalgebra? Obviously, in this case, the ...
20
QHWM of the orthogonal and symplectic types Lie subalgebras of the Lie algebra of the matrix quantum pseudo differential operators
... The dificulty when studying the representation theory of these algebras lies in the fact that, although they admit a Z -gradation and a triangular decomposition, each of the graded subspaces is still infinite ...
36
Estructura de los productos tensoriales de sl(2) n V (m)-módulos uniseriales
... algebra de Lie perfectas sl(2) n V (m) donde V (m) es un sl(2)-m´ odulo de peso m´ aximo m ≥ 1. Esta clasificaci´ on est´ a completamente determinada por una familia de m´ odulos uniseriales denotados Z(a, `) y ...
128
Estructuras localmente conformes Kähler y localmente conformes simplécticas en solvariedades compacta
... de Lie con una estructura sasakiana (h· , · i, φ, η, ξ), en este caso ξ se llama el vector de Reeb, y adem´ as, es f´ acil verificar que el centro de h tiene dimensi´ on a lo sumo ...
126
Teorema del peso máximo
... En el Cap´ıtulo 6 mostramos c´ omo funciona el Teorema en tres ejemplos. El primero es el ´ algebra de Lie sl(3, C ), el m´ as simple despu´ es del de sl(2, C ), ya tratado. El segundo es el grupo SU(2); por ser ...
55
Prime ideals of skew PBW extensions
... Weyl algebras, enveloping algebras of finite-dimensional Lie algebras (and their quantiza- tions), Artamonov quantum polynomials, diffusion algebras, and Manin al- gebra of quantum ...
17