Abstract:

Based on the ideas of noncommutative geometry, we think about a graded associative algebra as a coordinate ring of a ``noncommutative projective variety''. The role of the category of coherent sheaves is played by the quotient of the category of graded finitely presented A-modules by the finite-dimensional ones. We demonstrate how to recover information about the algebra from its bounded derived category in the case of monomial and path algebras. In particular, we calculate the entropy in graphs, algebras, and derived categories.