The Surjective H-Colouring problem is to test if a given graph allows a vertex-surjective homomorphism to a fixed graph H. The complexity of this problem has been well studied for undirected (partially) reflexive graphs. We introduce endo-triviality, the property of a structure that all of its endomorphisms that do not have range of size 1 are automorphisms, as a means to obtain complexity-theo...

The aim of this paper is to show that the automorphism and isometry groups of the suspension of B(H), H being a separable infinite dimensional Hilbert space, are algebraically reflexive. This means that every local automorphism, respectively local surjective isometry of C0(R) ⊗ B(H) is an automorphism, respectively a surjective isometry.

We deeply analyse the structural organisation of the fibration of points and of the monad of internal groupoids. From that we derive: 1) a new characterization of internal groupoids among reflexive graphs in the Mal’cev context; 2) a setting in which a Mal’cev category is necessarily a protomodular category.

We give a brief overview of the axiomatic development of betweenness relations, and investigate the connections between these and comparability graphs. Furthermore, we characterize betweenness relations induced by reflexive and antisymmetric binary relations, thus generalizing earlier results on partial orders. We conclude with a sketch of the algorithmic aspects of recognizing induced betweenn...

We introduce the concept of neighborhood systems as a generalization of directed, reflexive graphs and show that the prime factorization of neighborhood systems with respect to the the direct product is unique under the condition that they satisfy an appropriate notion of thinness.

a matrix $pintextmd{c}^{ntimes n}$ is called a generalized reflection matrix if $p^{h}=p$ and $p^{2}=i$‎. ‎an $ntimes n$‎ ‎complex matrix $a$ is said to be a reflexive (anti-reflexive) matrix with respect to the generalized reflection matrix $p$ if $a=pap$ ($a=-pap$)‎. ‎in this paper‎, ‎we introduce two iterative methods for solving the pair of matrix equations $axb=c$ and $dxe=f$ over reflexiv...

We define very proper intersections of modules and projective subschemes. It turns out that equidimensional locally Cohen-Macaulay modules intersect very properly if and only if they intersect properly. We prove a Bezout theorem for modules which meet very properly. Furthermore, we show for equidimensional subschemes X and Y : If they intersect properly in an arithmetically Cohen-Macaulay subsc...

In this paper we answer a question raised in [Mol] by giving an example of a proper standard C∗-subalgebra of B(H) whose automorphism and isometry groups are topologically reflexive. After this we prove that in the case of extensions of the C∗-algebra C(H) of all compact operators by separable commutative C∗algebras, these groups are algebraically reflexive. Concerning the most well-known exten...