Claudia Gallego

My principal research areas are related with computational algebra and non-commutative ring theory. Specifically, I have been working with non-commutative Gröbner bases for some algebras of polynomial type, besides developing several algorithms for computing projective dimension, bases for free modules, tools for determining whether a given module is stably free, and another similar results. In addition, I have studied the behavior of finitely generated projective modules over various class of rings, and topics related as non-commutative localizations, homological dimensions and diverse stabilization problems.

Currently, I am studying representations of Generalized Weyl Algebras, classification of Hopf algebras from a categorical point of view, Hopf actions over algebras similar to Weyl algebras and the stable rank of several associative algebras defined by polynomial relations.

Other research interests are related with algebraic topology, algebraic geometry, differential geometry, Lie algebras and several topics of Mathematical Physics.