We study the Lie module structure given by the Gerstenhaber bracket on the Hochschild cohomology groups of a monomial algebra with radical square zero. The description of such Lie module structure will be given in terms of the combinatorics of the quiver. The Lie module structure will be related to the classification of finite dimensional modules over simple Lie algebras when the quiver is give...

A planar monomial is by definition an isomorphism class of a finite, planar, reduced rooted tree. If x denotes the tree with a single vertex, any planar monomial is a non-associative product in x relative to m−array grafting. A planar power series f(x) over a field K in x is an infinite sum of K−multiples of planar monomials including the unit monomial represented by the empty tree. For every p...

Nonlinearity of rotation symmetric Boolean functions is an important topic on cryptography algorithm. Let e ≥ 1 be any given integer. In this paper, we investigate the following question: Is the nonlinearity of the quartic rotation symmetric Boolean function generated by the monomial x0xex2ex3e equal to its weight? We introduce some new simple sub-functions and develop new technique to get seve...