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Displaying 161 – 180 of 252

On the doubling of quadratic algebras

Lars Lindberg (2004)

Colloquium Mathematicae

The concept of doubling, which was introduced around 1840 by Graves and Hamilton, associates with any quadratic algebra 𝓐 over a field k of characteristic not 2 its double 𝓥(𝓐 ) = 𝓐 × 𝓐 with multiplication (w,x)(y,z) = (wy - z̅x,xy̅ + zw). This yields an endofunctor on the category of all quadratic k-algebras which is faithful but not full. We study in which respect the division property of a quadratic k-algebra is preserved under doubling and, provided this is the case, whether the...

On the Enright-Varadarajan modules : a construction of the discrete series

Nolan R. Wallach (1976)

Annales scientifiques de l'École Normale Supérieure

On the exponential representation of $G L_{p, q} (1 | 1)$ .

Çelik, Sultan A., Gülten, Dilek (2002)

Balkan Journal of Geometry and its Applications (BJGA)

On the formula of Ślebodziński for Lie derivative of tensor fields in a differential space

Hanna Matuszczyk (1982)

Colloquium Mathematicae

On the Gel'fand-Kirillov conjecture for induced ideals in the semisimple case

Anthony Joseph (1979)

Bulletin de la Société Mathématique de France

On the geometric prequantization of brackets.

Manuel de León, Juan Carlos Marrero, Edith Padrón (2001)

RACSAM

En este artículo se considera un marco general para la precuantización geométrica de una variedad provista de un corchete que no es necesariamente de Jacobi. La existencia de una foliación generalizada permite definir una noción de fibrado de precuantización. Se estudia una aproximación alternativa suponiendo la existencia de un algebroide de Lie sobre la variedad. Se relacionan ambos enfoques y se recuperan los resultados conocidos para variedades de Poisson y Jacobi.

On the geometry of conjugacy classes in classical groupes.

Hanspeter Kraft, Claudio Procesi (1982)

Commentarii mathematici Helvetici

On the ghost centre of Lie superalgebras

Maria Gorelik (2000)

Annales de l'institut Fourier

We study the invariants of the universal enveloping algebra of a Lie superalgebra with respect to a certain “twisted” adjoint action.

On the Hattori-Stallings trace for certain primitive factors of enveloping algebras of semisimple Lie algebras.

Gadi S. Perets, Patrick Polo (1995)

Mathematische Zeitschrift

On the homology of free Lie algebras

Calin Popescu (1998)

Commentationes Mathematicae Universitatis Carolinae

Given a principal ideal domain $R$ of characteristic zero, containing $1 / 2$ , and a connected differential non-negatively graded free finite type $R$ -module $V$ , we prove that the natural arrow $𝕃 F H (V) \to F H 𝕃 (V)$ is an isomorphism of graded Lie algebras over $R$ , and deduce thereby that the natural arrow $U F H 𝕃 (V) \to F H U 𝕃 (V)$ is an isomorphism of graded cocommutative Hopf algebras over $R$ ; as usual, $F$ stands for free part, $H$ for homology, $𝕃$ for free Lie algebra, and $U$ for universal enveloping algebra. Related facts and examples are also considered....

On the homology of free nilpotent Lie algebras.

Tirao, Paulo (2002)

Journal of Lie Theory

On the homology of SL..., a complement.

Jean-Luis Cathelineau (1990)

Mathematica Scandinavica

On the infinitesimal kernel of irreducible representations of nilpotent Lie groups

Niels Vigand Pedersen (1984)

Bulletin de la Société Mathématique de France

On the joint spectral radius of a nilpotent Lie algebra of matrices

Enrico Boasso (1999)

Studia Mathematica

For a complex nilpotent finite-dimensional Lie algebra of matrices, and a Jordan-Hölder basis of it, we prove a spectral radius formula which extends a well-known result for commuting matrices.

On the Joseph-small additivity principle for goldie ranks. A study on extensions of noetherian rings with applications to enveloping algebras

Walter Borho (1982)

Compositio Mathematica

On the $K$ -theory and Hattori-Stallings traces of minimal primitive factors of enveloping algebras of semisimple Lie algebras : the singular case

Patrick Polo (1995)

Annales de l'institut Fourier

Let $G$ be a semisimple complex algebraic group and $X$ its flag variety. Let $𝔤 = Lie (G)$ and let $U$ be its enveloping algebra. Let $𝔥$ be a Cartan subalgebra of $𝔤$ . For $μ \in 𝔥^{*}$ , let $J_{μ}$ be the corresponding minimal primitive ideal, let $U_{μ} = U / J_{μ}$ , and let $𝒯_{U_{μ}} : K_{0} (U_{m} u) \to ℂ$ be the Hattori-Stallings trace. Results of Hodges suggest to study this map as a step towards a classification, up to isomorphism or Morita equivalence, of the $ℂ$ -algebras $U_{μ}$ . When $μ$ is regular, Hodges has shown that $K_{0} (U_{μ}) ≅ K_{0} (X)$ . In this case $K_{0} (U_{μ})$ is generated by the classes corresponding to...

On the Lebesgue decomposition of the normal states of a JBW-algebra

Jacques Dubois, Brahim Hadjou (1992)

Mathematica Bohemica

In this article, a theorem is proved asserting that any linear functional defined on a JBW-algebra admits a Lebesque decomposition with respect to any normal state defined on the algebra. Then we show that the positivity (and the unicity) of this decomposition is insured for the trace states defined on the algebra. In fact, this property can be used to give a new characterization of the trace states amoungst all the normal states.

On the Lie algebra of holomorphic infinitesimal isometries of some classical complex symmetric Banach manifolds

José Isidro (2007)

Open Mathematics

The Banach-Lie algebras ℌκ of all holomorphic infinitesimal isometries of the classical symmetric complex Banach manifolds of compact type (κ = 1) and non compact type (κ = −1) associated with a complex JB*-triple Z are considered and the Lie ideal structure of ℌκ is studied.

On the Lie algebra of vertical prolongation operators

Josef Janyška (1982)

Czechoslovak Mathematical Journal

On the minimal canonical realizations of the Lie algebra $O_{c} (n)$

M. Havlíček, P. Exner (1975)

Annales de l'I.H.P. Physique théorique

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