Quantum Groups

Quantum groups are advanced mathematical structures that extend traditional symmetries found in physics and mathematics, capturing how systems behave at quantum scales. Unlike classical groups that describe symmetry and conservation laws, quantum groups incorporate the principles of quantum mechanics, where properties can be probabilistic and interconnected. They are useful in understanding complex phenomena such as quantum integrable systems, knot theory, and statistical mechanics, by providing a framework that generalizes and deforms classical symmetry concepts to fit the quantum realm. This helps in tackling problems where classical assumptions no longer hold, revealing deeper insights into the underlying structure of nature.