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Physics at the FQMT`04 conference
Physics at the FQMT`04 conference

... thermodynamics had to take into account additional ingredients, but the overall structure of thermodynamics and its laws, and its meaning as the method of description of huge, macroscopic systems, remained unchanged since it was believed that quantum mechanics does not play a role at the macroscopic ...
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... computer therefore threatens the security of past and present communication as well as electronic commerce. Therefore, the academic, the commercial and the strategic points of view require that Brazil increase its efforts and pursue the state of the art in this highly international field. In order ...
Conclusive exclusion of quantum states
Conclusive exclusion of quantum states

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Quantum group

In mathematics and theoretical physics, the term quantum group denotes various kinds of noncommutative algebra with additional structure. In general, a quantum group is some kind of Hopf algebra. There is no single, all-encompassing definition, but instead a family of broadly similar objects.The term ""quantum group"" first appeared in the theory of quantum integrable systems, which was then formalized by Vladimir Drinfeld and Michio Jimbo as a particular class of Hopf algebra. The same term is also used for other Hopf algebras that deform or are close to classical Lie groups or Lie algebras, such as a `bicrossproduct' class of quantum groups introduced by Shahn Majid a little after the work of Drinfeld and Jimbo.In Drinfeld's approach, quantum groups arise as Hopf algebras depending on an auxiliary parameter q or h, which become universal enveloping algebras of a certain Lie algebra, frequently semisimple or affine, when q = 1 or h = 0. Closely related are certain dual objects, also Hopf algebras and also called quantum groups, deforming the algebra of functions on the corresponding semisimple algebraic group or a compact Lie group.Just as groups often appear as symmetries, quantum groups act on many other mathematical objects and it has become fashionable to introduce the adjective quantum in such cases; for example there are quantum planes and quantum Grassmannians.
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