1,721,013 research outputs found
Anew proof of the J^2 condition for real rank one simple Lie algebras
No full textIn this paper a new purely algebraic proof of the J^2-condition for the nilpotent Iwasawa algebras in real rank one simple Lie algebras is presented, yielding the classification of real rank one simple Lie algebras
A Clifford algebra approach to real simple Lie algebras, I: The algebras with reduced root system
No full textIn this paper we classiy real simple Lie algebras with reduced root system, i.e.
the algebras with a root system belonging to one of the families Ar , Br , Cr , Dr (r
∈ N), Er (r =
6, 7, 8), F4 , G2 .
We use the tools of Clifford
algebra classification, and derive the formulae for the root multiplicities. For the classical cases
we indicate explicit models of matrix algebras with the derived root multiplicities
A Clifford algebra approach to real rank one simple Lie algebras: The G_2 case
No full textLet g = k ⊕ a ⊕ n be an Iwasawa decomposition for a simple real Lie algebra g.
It is known that the subalgebra a ⊕ n determines g. In this paper we show how to construct g starting from the root system for the pair (g, a) whenever this root system is of type G2 .
We use, in particular, Clifford algebra and the spin representation.
We compute an explicit linear basis for the split, simple, real Lie algebra of type G2 and
determine the structure constants
Scalar products on Clifford modules and pseudo-H-type Lie algebras
No full textIn 1980 A. Kaplan introduced the so called generalised Heisenberg algebras, which
are two step nilpotent algebras endowed with an inner product satisfying a compatibility
condition with the Lie algebra structure. In this paper we generalize the definition of tk Ka-
plan to the case of a nonpositive definite scalar product. In the non-positive definite case the
proof of the existence and the classification raise entirely new problems. The natural setting
to solve them is that of the theory of Clifford modules
Spherical distributions on harmonic extensions of pseudo-H-type groups
No full textIn the articles "Ciatti, P., Scalar products on Clifford modules and pseudo-H-type Lie algebras, Ann. Mat. Pura Appl., to appear" and "Ciatti, P., Solvable extensions of pseudo-H-type algebras, Boll. Un. Mat. It., to appear," a class of solvable pseudo-Riemannian harmonic manifolds was constructed. Now spherical distributions on such manifolds are investigated. A notion of radiality for distributions is introduced with the aid of a technique due to J. Faraut (Faraut, J., Distributions sphérique sur les espaces hyperboliques, J. Math. Pures Appl., (1979), 369-444). The spherical distributions are the radial eigendistributions of the Laplace-Beltrami operator. They span a space which, depending on the signature of the metric, may have dimension one or two
A Clifford algebra approach to simple Lie algebras of real rank two, I; the A_2 case
No full textBy using Clifford algebraic methods, we classify all real semisimple Lie algebras of type A(2). This approach to the classification avoids the need to discuss the real and complex cases separately, and also provides interesting information about the structure of the algebras
A Clifford algebra approach to real rank one simple Lie algebras
No full textIn this paper, we continue our work to classify and describe real simple Lie algebras
based on the analysis of an Iwasawa nilpotent subalgebra n of g. We consider real
rank one simple Lie algebras and then study generalized Heisenberg algebras to describe the
structure of g based on n
A Clifford algebra approach to real simple Lie algebras. II. The algebras with root system BCr .
No full textThe paper deals with the classification of real simple BC_r Lie algebras. We study the
Clifford modules that naturally arise in real simple Lie algebras.
In particular, by using the well-known isomorphisms among low-dimensional
compact groups and induction, we classify algebras with root system
BC_r
L^p joint eigenfunction bounds on quaternionic spheres
No full textWe prove some sharp L^p-L^2 estimates for joint spectral projections, for p between 1 and 2,
associated to the Laplace--Beltrami operator and to a suitably defined subLaplacian
on the unit quaternionic sphere
Restriction estimates for the full Laplacian on Métivier groups
Full text linkIn this paper we prove a restriction theorem for
the full Laplacian on
a group of Métivier type. In particular,
we compute the spectral resolution of this operator and estimate
the norm of the spectral projections
between Lebesgue spaces
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