Alejandro Tiraboschi

Classes of 2-step nilpotent lie algebras

We give a characterization of the Lie algebras of H-type independent of the inner product used in the definition. We classify the real 2-step nilpotent Lie algebras with 2-dimensional center. Using...

Regular Metabelian Lie Algebras

We use a new characterization of the Lie algebras of H-type and the classification of regular 2-step nilpotent Lie algebras of center 2 to produce examples of regular Lie algebras that are not H-type.

Quantum Heisenberg groups and sklyanin algebras

New bialgebra structures on the Heisenberg-Lie algebra and their quantizations are introduced. Some of these quantizations give rise to new multiplications in homogeneous coordinate rings of Abelian varieties, via the well-known identification of theta functions with suitable matrix coefficients of the Stone-von Neumann representations.

On gelfand-kirillov dimensions (g,A) of modules

Let Gbe a real connected semisimple real Lie group and let be Aa connected reductive subgroupg,athe complexified Lie algebras of Gand A respectively; assume (g,a) is a regular pair.In this paper we study general properties of (g, A)-modules, and we prove for two particular cases that every admissible (g, A)-module with an infinitesimal character has finite length.We also compute Gelfand-Kiriilov dimensions for some modules and a number (Vogans dimension) related to it.Finally we construct a virtual (g,A)-module with“minimal”Vogans dimension.