Thanks Pavel Etingof! But what is a partical ? how to difine it ? Are symmetries needed to difine particals? Should they be the irreducible representions?

Theo Johnson-Freyd said : the short answer is that "quantum groups" were invented in the study of quantum integrable systems. quantum integrable systems,as far as my best understand from mathmatical viewpoint,are just algbras of observables with sufficent symmetries and the hilbert space of states is the module of algbra of observables. My questions are: 1 Are algbras of observables quantum groups? 2 What are the symmetry of these systems? the symmetry of algebra of observables or the symmetry of the module ? 3 What is the relation between symmetry and quantum group?

I know that quantum groups are just hopf algebtras which are bialgebras with antipode and some compatible conditions and coproducts are essential to define tensor product of modules so that the moudle category become a tensor category. But I don't know how to interpret tensor product in physical language.