Algorithmic Methods in Non-Commutative Algebra: Applications by J.L. Bueso,José Gómez-Torrecillas,A. Verschoren

By J.L. Bueso,José Gómez-Torrecillas,A. Verschoren

The already huge variety of purposes of ring idea has been more desirable within the eighties through the expanding curiosity in algebraic buildings of substantial complexity, the so-called category of quantum teams. one of many primary houses of quantum teams is they are modelled via associative coordinate earrings owning a canonical foundation, which permits for using algorithmic constructions according to Groebner bases to check them. This ebook develops those tools in a self-contained approach, focusing on an in-depth examine of the thought of an unlimited classification of non-commutative earrings (encompassing such a lot quantum groups), the so-called Poincaré-Birkhoff-Witt earrings. We contain algorithms which deal with crucial elements like beliefs and (bi)modules, the calculation of homological measurement and of the Gelfand-Kirillov size, the Hilbert-Samuel polynomial, primality assessments for top beliefs, etc.

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