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Moduli of unipotent representations I: foundational topics

Ishai Dan-Cohen (2012)

Annales de l’institut Fourier

With this work and its sequel, Moduli of unipotent representations II, we initiate a study of the finite dimensional algebraic representations of a unipotent group over a field of characteristic zero from the modular point of view. Let G be such a group. The stack ℳ n ( G ) of all representations of dimension n is badly behaved. In this first installment, we introduce a nondegeneracy condition which cuts out a substack ℳ n nd ( G ) which is better behaved, and, in particular, admits a coarse algebraic space, which...

Multi-dimensional Cartan prolongation and special k-flags

Piotr Mormul (2004)

Banach Center Publications

Since the mid-nineties it has gradually become understood that the Cartan prolongation of rank 2 distributions is a key operation leading locally, when applied many times, to all so-called Goursat distributions. That is those, whose derived flag of consecutive Lie squares is a 1-flag (growing in ranks always by 1). We first observe that successive generalized Cartan prolongations (gCp) of rank k + 1 distributions lead locally to all special k-flags: rank k + 1 distributions D with the derived...

Nilpotent complex structures.

Luis A. Cordero, Marisa Fernández, Alfred Gray, Luis Ugarte (2001)

RACSAM

Este artículo presenta un panorama de algunos resultados recientes sobre estructuras complejas nilpotentes J definidas sobre nilvariedades compactas. Tratamos el problema de clasificación de nilvariedades compactas que admiten una tal J, el estudio de un modelo minimal de Dolbeault y su formalidad, y la construcción de estructuras complejas nilpotentes para las cuales la sucesión espectral de Frölicher no colapsa en el segundo término.

Nilpotent control systems.

Elisabeth Remm, Michel Goze (2002)

Revista Matemática Complutense

We study the class of matrix controlled systems associated to graded filiform nilpotent Lie algebras. This generalizes the non- linear system corresponding to the control of the trails pulled by car.

Normal and Normally Outer Automorphisms of Free Metabelian Nilpotent Lie Algebras

Fιndιk, Şehmus (2010)

Serdica Mathematical Journal

2000 Mathematics Subject Classification: 17B01, 17B30, 17B40.Let Lm,c be the free m-generated metabelian nilpotent of class c Lie algebra over a field of characteristic 0. An automorphism φ of Lm,c is called normal if φ(I) = I for every ideal I of the algebra Lm,c. Such automorphisms form a normal subgroup N(Lm,c) of Aut (Lm,c) containing the group of inner automorphisms. We describe the group of normal automorphisms of Lm,c and the quotient group of Aut (Lm,c) modulo N(Lm,c).

On a nilpotent Lie superalgebra which generalizes Qn.

José María Ancochea Bermúdez, Otto Rutwig Campoamor (2002)

Revista Matemática Complutense

In Gilg (2000, 2001) the author introduces the notion of filiform Lie superalgebras, generalizing the filiform Lie algebras studied by Vergne in the sixties. In these appers, the superalgebras whose even part is isomorphic to the model filiform Lie algebra Ln are studied and classified in low dimensions. Here we consider a class of superalgebras whose even part is the filiform, naturally graded Lie algebra Qn, which only exists in even dimension as a consequence of the centralizer property. Certain...

On dimension of the Schur multiplier of nilpotent Lie algebras

Peyman Niroomand (2011)

Open Mathematics

Let L be an n-dimensional non-abelian nilpotent Lie algebra and s ( L ) = 1 2 ( n - 1 ) ( n - 2 ) + 1 - dim M ( L ) where M(L) is the Schur multiplier of L. In [Niroomand P., Russo F., A note on the Schur multiplier of a nilpotent Lie algebra, Comm. Algebra (in press)] it has been shown that s(L) ≥ 0 and the structure of all nilpotent Lie algebras has been determined when s(L) = 0. In the present paper, we will characterize all finite dimensional nilpotent Lie algebras with s(L) = 1; 2.

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