The Pukánszky invariant associates to each maximal abelian self–adjoint subalgebra (masa) A in a type II1 factor M a certain subset ot N ∪ {∞}, denoted Puk(A). We study this invariant in the context of factors generated by infinite conjugacy class discrete countable groups G with masas arising from abelian subgroups H. Our main result is that we are able to describe Puk(V N(H)) in terms of the ...

1. Introduction. Let p be a prime number and F an algebraic closure of the finite field F p with p elements. Let n and N denote positive integers, N prime to p. We are interested in representations ρ of the Galois group G Q = Gal(¯ Q/Q) into GL(n, F), unramified at all finite primes not dividing pN. (We shall say ρ is unramified outside pN.) In this paper, representation will always mean contin...

In 2012, Aaronson and Christiano introduced the idea of hidden subspace states to build public-key quantum money [STOC ’12]. Since then, this has been applied realize several other cryptographic primitives which enjoy some form unclonability.

We characterize which permutational wreath products G⋉W (X) are finitely presented. This occurs if and only if G and W are finitely presented, G acts on X with finitely generated stabilizers, and with finitely many orbits on the cartesian square X. On the one hand, this extends a result of G. Baumslag about infinite presentation of standard wreath products; on the other hand, this provides nont...

Kwak, J.H. and J. Lee, Isomorphism classes of cycle permutation graphs, Discrete Mathematics 105 (1992) 131-142. In this paper, we construct a cycle permutation graph as a covering graph over the dumbbell graph, and give a new characterization of when two given cycle permutation graphs are isomorphic by a positive or a negative natural isomorphism. Also, we count the isomorphism classes of cycl...