Jan 12, 2018 · Quantum algebra is an umbrella term used to describe a number of different mathematical ideas, all of which are linked back to the original realisation that in quantum physics, …

Having heard of the 'small quantum group' and Lusztigs algebra U dot (notation in his quantum groups book), I suspect the existence of multiple approaches, which diverge at least when an integral form is …

Quantum Groups and Their Representations, by Anatoli Klimyk and Konrad Schmudgen. They have a penchant for doing things in excruciating, unenlightening formulas, but this book is the first one that I …

Feb 17, 2025 · I am trying to understand how one can perform second quantization in the case of the Hamiltonian of the hydrogen atom, i.e. when the one particle Hamiltonian acquires an external …

Oct 21, 2025 · The algebra $\widehat {U_q (\mathfrak {sl}_2)}$ is then its $ (q-1)$-adic completion, making it a topological algebra over $\mathbb {C} [ [q-1]]$. And yes, the tensor product in the …

Quantum groups are the main algebraic way to understand the quantum polynomial invariants of knots and links; and quantum groups at roots of unity are the main algebraic way to understand the …

Apr 8, 2025 · qa.quantum-algebra quantum-groups hopf-algebras poisson-geometry See similar questions with these tags.

Mar 24, 2021 · Another well-known example of a non-commutative non-co-commutative finite quantum group is the Kac–Paljutkin quantum group, which is the smallest-dimensional such finite quantum …

Hence, quantum mathematics has something to do with perturbation theory, because most of the interesting objects in quantum mathematics are perturbations of trivial solutions of some …

In the same vein as Kate and Scott 's questions, why are fusion categories interesting? I know that given a "suitably nice" fusion category (which probably means adding adjectives such as "unitary," …