Using the Kramer-Mesner method, 4-(26, 6, λ) designs with PSL(2, 25) as a group of automorphisms and with λ in the set {30, 51, 60, 81, 90, 111} are constructed. The search uses specific partitioning of columns of the orbit incidence matrix, related to so-called “quasi-designs”. Actions of groups PSL(2, 25), PGL(2, 25) and twisted PGL(2, 25) are being compared. It is shown that there exist 4-(2...

We initiate a detailed and systematic study of automorphisms of the Cuntz algebras On which preserve both the diagonal and the core UHF -subalgebra. A general criterion of invertibility of endomorphisms yielding such automorphisms is given. Combinatorial investigations of endomorphisms related to permutation matrices are presented. Key objects entering this analysis are labeled rooted trees equ...

Recently Umirbaev has proved the long-standing Anick conjecture, that is, there exist wild automorphisms of the free associative algebra K〈x, y, z〉 over a field K of characteristic 0. In particular, the well-known Anick automorphism is wild. In this article we obtain a stronger result (the Strong Anick Conjecture that implies the Anick Conjecture). Namely, we prove that there exist wild coordin...

We demonstrate the usefulness of projection matrices for finite subalgebras h c 3 and their affine counterparts h c i in finding field identifications (and selection rules) in coset conformal field theories. Submitted to Phys. Lett. B. * Work supported by the U.S. Department of Energy under Contract DE-AC0376SF00515. Address after September 1, 1989: Newman Laboratory of Nuclear Studies, Cornell...

Cluster automorphisms have been shown to have links to the mapping class groups of surfaces, maximal green sequences and to exchange graph automorphisms for skew-symmetric cluster algebras. In this paper we generalise these results to the skew-symmetrizable case by introducing a marking on the exchange graph. Many skew-symmetrizable matrices unfold to skew-symmetric matrices and we consider how...

The present paper investigates the groups of automorphisms for some lattices of modal logics. The main results are the following. The lattice of normal extensions of S4.3, NExtS4.3, has exactly two automorphisms, NExtK.alt1 has continuously many automorphisms. Moreover, any automorphism of NExtS4 fixes all logics of finite codimension. We also obtain the following characterization of pretabular...

Let G be the group of order-preserving automorphisms of the rationals Q, or the group of colour-preserving automorphisms of the C-coloured random graph RC . We show that given any non-identity f ∈ G, there exists g ∈ G such that every automorphism in G is the limit of a sequence of automorphisms generated by f and g. Moreover, if, in some sense, f has no finite structure, then g can be chosen w...

Certain classes of automorphisms of reduced amalgamated free products of C∗– algebras are shown to have Brown–Voiculescu topological entropy zero. Also, for automorphisms of exact C∗–algebras, the Connes–Narnhofer–Thirring entropy is shown to be bounded above by the Brown–Voiculescu entropy. These facts are applied to generalize Størmer’s result about the entropy of automorphisms of the II1–fac...

For a fixed odd prime p and a representation ̺ of the absolute Galois group of Q into the projective group PGL2(Fp), we provide the twisted modular curves whose rational points supply the quadratic Q-curves of degree N prime to p that realize ̺ through the Galois action on their p-torsion modules. The modular curve to twist is either the fiber product of the modular curves X0(N) and X(p) or a cer...