By Eric Jespers, Jan Okninski

Within the decade, semigroup theoretical tools have happened certainly in lots of points of ring conception, algebraic combinatorics, illustration idea and their functions. particularly, inspired via noncommutative geometry and the speculation of quantum teams, there's a becoming curiosity within the classification of semigroup algebras and their deformations.

This paintings offers a complete therapy of the most effects and strategies of the idea of Noetherian semigroup algebras. those common effects are then utilized and illustrated within the context of significant periods of algebras that come up in various parts and feature been lately intensively studied. a number of concrete structures are defined in complete element, particularly fascinating sessions of quadratic algebras and algebras regarding staff earrings of polycyclic-by-finite teams. those supply new periods of Noetherian algebras of small Gelfand-Kirillov measurement. the focal point is at the interaction among their combinatorics and the algebraic constitution. This yields a wealthy source of examples which are of curiosity not just for the noncommutative ring theorists, but additionally for researchers in semigroup thought and sure facets of crew and staff ring thought. Mathematical physicists will locate this paintings of curiosity as a result of the eye given to applications to the Yang-Baxter equation.