By S. Duplij
The strategies of noncommutative space-time and quantum teams have foundgrowing awareness in quantum box conception and string concept. The mathematical ideas of quantum teams were a ways constructed through mathematicians and physicists of the japanese eu nations. in particular, V. G. Drinfeld fromUkraine, S. Woronowicz from Poland and L. D. Faddeev from Russia have beenpioneering the sector. it kind of feels to be usual to collect those scientists with researchers in string idea and quantum box conception of the Western eu international locations. From one other part, supersymmetry, as one in every of examples of noncommutative constitution, used to be stumbled on in early 70's within the West via J. Wess (one of the co-Directors) and B. Zumino and within the East through physicists from UkraineV. P. Akulov and D. V. Volkov. for that reason, Ukraine appears to be like a typical position to satisfy.
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31 SYMMETRIES WIDER THAN SUPERSYMMETRY 25 3. Appendix. 1. In what follows all the algebras are associative with unit over a field K, char K = 2. We will deal with two important PI-varieties of algebras (the varieties singled out by polynomial identities): – the variety C of supercommutative superalgebras; – the variety G generated (by tensoring and passing to quotients) by the Grassmann algebra Λ(∞) of countably many indeterminates (its natural Z/2-grading ignored). The variety G plays a significant role in the theory of varieties of associative algebras ([21]).
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