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

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

The already vast variety of functions of ring concept has been more desirable within the eighties by way of the expanding curiosity in algebraic constructions of substantial complexity, the so-called classification 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 in response to Groebner bases to review them. This ebook develops those tools in a self-contained manner, targeting an in-depth research of the concept of an enormous 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 features like beliefs and (bi)modules, the calculation of homological measurement and of the Gelfand-Kirillov size, the Hilbert-Samuel polynomial, primality checks for top beliefs, etc.

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