A note on the positive Schur property

A Note on Frobenius-schur Indicators

This exposition concerns two different notions of Frobenius-Schur indicators for finite-dimensional Hopf algebras. These two versions of indicators coincide when the underlying Hopf algebra is semisimple. We are particularly interested in the family of pivotal finite-dimensional Hopf algebras with unique pivotal element; both indicators are gauge invariants of this family of Hopf algebras. We o...

Schur-Pair Property and the Structure of Varietal Covering Groups

A Note on the Four-point Property

x = niabcfghpqr, y = nigh(af) 2 p*, z = mca(bg) 2 q s , w = tnbf{ch) 2 r z , where the parameters m, • • • , r may be restricted by the G.CD. conditions 1 = (o,f) = (b,g) = (c,h), 1 = (afp, bcqr) = (bgq, hfrp) = (chr, agpq). The most immediate application of this is to the solution of # 3 +/(:y> £> «0 = 0> where ƒ (y, z, w) is any ternary cubic factorable into 3 linear, homogeneous factors whos...

A Note on the Ramsey Property

An elementary setting of the classical Ramsey property is given, which leads to simple proofs of the relevant theorems of Galvin-Prikry and Silver.

A note on verifying the APN property

We show that for an arbitrary mapping F on F2 to verify that it is APN, it is enough to consider the difference mappings of F defined by elements from an hyperplane.