By Eric Jespers, Jan Okninski
Within the decade, semigroup theoretical tools have happened evidently in lots of features of ring thought, algebraic combinatorics, illustration idea and their functions. particularly, influenced by means of noncommutative geometry and the idea of quantum teams, there's a turning out to be curiosity within the category of semigroup algebras and their deformations.
This paintings provides a complete therapy of the most effects and techniques of the speculation of Noetherian semigroup algebras. those common effects are then utilized and illustrated within the context of significant periods of algebras that come up in quite a few parts and feature been lately intensively studied. a number of concrete structures are defined in complete element, specifically interesting sessions of quadratic algebras and algebras with regards to staff earrings of polycyclic-by-finite teams. those supply new sessions of Noetherian algebras of small Gelfand-Kirillov size. the point of interest 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 in addition for researchers in semigroup concept and likely points of team and team ring thought. Mathematical physicists will locate this paintings of curiosity because of the eye given to applications to the Yang-Baxter equation.
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