In this paper we study the tensor powers of standard representation quantum super-algebra $U_q(sl(2|1)$, focusing on rings its algebra endomorphisms, called centraliser algebras and denoted by $LG_n$. Their dimensions were conjectured I. Marin E. Wagner \cite{MW}. We prove conjecture, describing intertwiner spaces from a semi-simple decomposition as sets consisting certain paths in planar latti...

Recently, public-key cryptography based on tropical semi-rings have been proposed. However, the majority of them are damaged. The main reason is that they use a public matrix to construct commutative semi-rings. New cryptosystems proposed in this paper. They congruent transformation symmetric by circular matrix. NP-hard problem solving system nonlinear equations underlies cryptosystem’s securit...