We introduce twisted Steinberg algebras over a commutative unital ring $R$. These generalise and are purely algebraic analogue of Renault's groupoid C*-algebras. In particular, for each ample Hausdorff $G$ locally constant $2$-cocycle $\sigma$ on taking values in the units $R^\times$, we study algebra $A_R(G,\sigma)$ consisting compactly supported $R$-valued functions $G$, with convolution invo...

The structure of the observable algebra OΛ of lattice QCD in the Hamiltonian approach is investigated. As was shown earlier, OΛ is isomorphic to the tensor product of a gluonic C∗-subalgebra, built from gauge fields and a hadronic subalgebra constructed from gauge invariant combinations of quark fields. The gluonic component is isomorphic to a standard CCR algebra over the group manifold SU(3)....

Triality theory is proved for a general unconstrained global optimization problem. The method adopted is simple but mathematically rigorous. Results show that if the primal problem and its canonical dual have the same dimension, the triality theory holds strongly in the tri-duality form as it was originally proposed. Otherwise, both the canonical min-max duality and the double-max duality still...

We consider the triality fusion category discovered in $c = 1$ KT theory \cite{Thorngren:2021yso}. analyze this using tools from group theoretical and describe how to compute simple lines, rules $F$-symbols. then study physical implication of including deriving spin selection rule, computing asymptotic density states irreps symmetries, analyzing its anomaly constraints on renormalization flow. ...