Given two finite p-local finite groups and a fusion preserving morphism between their Sylow subgroups, we study the question of extending it to a continuous map between the classifying spaces. The results depend on the construction of the wreath product of p-local finite groups which is also used to study p-local permutation representations.

Recently, Hu and Jia presented an efficient attack on the GGH13 map. They show that the MPKE and WE based on GGH13 with public tools of encoding are not secure. Currently, an open problem is to fix GGH13 with functionality-preserving. By modifying zero-testing parameter and using switching modulus method, we present a new construction of multilinear map from ideal lattices. Our construction mai...

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products {a, b, c} = (abc + cba)/2. These include especially isometries and disjointness preserving operators.

We prove that the stationarity and the ergodicity of a quantum source {ρ[1,m]}m=1 are preserved by any trace-preserving completely positive linear map of the tensor product form E⊗m, where a copy of E acts locally on each spin lattice site. We also establish ergodicity criteria for so called classically-correlated quantum sources.

We demonstrate the way to derive second Painlevé equation P2 and its Bäcklund transformations from deformations of Nonlinear Schrödinger (NLS), all while preserving strict invariance with respect Schlesinger transformations. The proposed algorithm allows for a construction Jordan algebra-based completely integrable multiple-field generalizations also producing corresponding suggest calling such...

We prove that Jordan triple elementary surjective maps on unital rings containing a nontrivial idempotent are automatically additive. The first result about the additivity of maps on rings was given by Martindale III in an excellent paper [7]. He established a condition on a ring R such that every multiplicative bijective map on R is additive. More precisely, he proved the following theorem. Th...

In this paper, we try to attack a conjecture of Araujo and Jarosz that every bijective linear map θ between C*-algebras, with both θ and its inverse θ−1 preserving zero products, arises from an algebra isomorphism followed by a central multiplier. We show it is true for CCR C*-algebras with Hausdorff spectrum, and in general, some special C*-algebras associated to continuous fields of C*-algebras.

Suppose that A is a C^*-algebra. We consider the class of A-linear mappins between two inner product A-modules such that for each two orthogonal vectors in the domain space their values are orthogonal in the target space. In this paper, we intend to determine A-linear mappings that preserve orthogonality. For this purpose, suppose that E and F are two inner product A-modules and A+ is the set o...

We take an algorithmic and computational approach to a basic problem in abstract algebra: determining the correct generalization to dialgebras of a given variety of nonassociative algebras. We give a simplified statement of the KP algorithm introduced by Kolesnikov and Pozhidaev for extending polynomial identities for algebras to corresponding identities for dialgebras. We apply the KP algorith...