Some su cient conditions for niteness of a generalized non abelian tensor product of groups are established extending Ellis result for compatible actions The non abelian tensor product of groups was introduced by Brown and Loday following works of A Lue and R K Dennis It was de ned for any groups A and B which act on themselves by conjugation y xyx and each of which acts on the other such that ...

It is known that if $$d^2$$ vectors in a d-dimensional Hilbert space H form symmetric, informationally complete, positive operator-valued measure (SIC-POVM), then the tensor squares of these an equiangular tight frame symmetric subspace $$H\otimes H$$ . We prove that, for any SIC-POVM Weyl–Heisenberg group covariant type (WH-type), this can be obtained by projecting WH-type basis onto subspace....

A partial difference set having parameters (n2, r(n − 1), n + r2 − 3r, r2 − r) is called a Latin square type partial difference set, while a partial difference set having parameters (n2, r(n + 1),−n + r2 + 3r, r2 + r) is called a negative Latin square type partial difference set. In this paper, we generalize well-known negative Latin square type partial difference sets derived from the theory o...

We calculate the polarization tensor of charged gluons in a Abelian homogeneous magnetic background field at finite temperature in one loop order Lorentz background field gauge in full generality. Thereby we first determine the ten independent tensor structures. For the calculation of the corresponding form factors we use the Schwinger representation and represent form factors as double paramet...

We propose a unified scheme to identify phase transitions out of the $\mathbb{Z}_2$ Abelian topological order, including transition non-Abelian chiral spin liquid. Using loop gas and string states [H.-Y. Lee, R. Kaneko, T. Okubo, N. Kawashima, Phys. Rev. Lett. 123, 087203 (2019)] on star lattice Kitaev model as an example, we compute overlap minimally entangled through transfer matrices. demons...

In this short note, we show that the class of abelian groups determined by the subgroup lattice of their direct n-powers is exactly the class of the abelian groups which share the n-root property. As applications we answer in the negative a (semi)conjecture of Palfy and solve a more general problem. Recently, for an arbitrary group G, the subgroup lattice of the square G×G has received some att...

We exhibit an algorithm to decide if the fixed-points of a morphism avoid (long) abelian repetitions and we use it to show that long abelian squares are avoidable over the ternary alphabet. This gives a partial answer to one of Mäkelä's questions. Our algorithm can also decide if a morphism avoids additive repetitions or k-abelian repetitions and we use it to show that long 2-abelian square are...