discipline

Pure Mathematics

subject

Homological Algebra

lecturers

István Ágoston, József Pelikán

credits

2

period

 

curriculum

The Hom and tensor functors (projective, injective and flat modules). Homological properties of special classes of rings (semisimple, von Neumann regular, hereditary, quasi-Frobenius rings). Homologies of complexes: homology groups, projective and injective resolutions. Derived functors (construction of Ext and Tor, basic properties). Exact sequences and the Ext functor (Yoneda product, Ext algebras). Homological dimensions (projective and injective dimension, global dimension, the Hilbert Syzygy Theorem, dominant dimension, Auslander algebras, finitistic dimension, the Finitistic Dimension Conjecture). Homological methods in the representation theory of algebras (almost split sequences, the Auslander–Reiten quiver). Derived categories (triangulated categories, chain complexes, the homotopy category, localization of categories, derived category of an algebra, Morita theory). Cohomolgy of groups. Spectral sequences (filtrations, bi-complexes, Künneths Theorems).

literature

Rotman: An Introduction to Homological Algebra

form of tuition

Lecture

mode of assessment

written/oral exam