Let L be an n-dimensional non-abelian nilpotent Lie algebra and $$ s(L)=\frac{1}{2}(n-1)(n-2)+1-\dim {\mathcal {M}}(L) where is the Schur multiplier of a L. The structures algebras when s(L)\in \lbrace 0,1,2,3,4,5\rbrace are determined. In this paper, we classify all s(L)=6,7.

C is called a completely bounded multiplier (= Herz-Schur multiplier) if the transformation defined on the linear span K(G) of {λ(x), x ∈ G} by x∈G f (x)λ(x) → x∈G f (x)ϕ(x)λ(x) is completely bounded (in short c.b.) on the C *-algebra C * λ (G) which is generated by λ (C * λ (G) is the closure of K(G) in B(ℓ 2 (G), ℓ 2 (G)).) One of our main results (stated below as Theorem 0.1) gives a simple ...

Abstract We prove that if G is a discrete group and $$(A,G,\alpha )$$ ( A , G α ) C*-dynamical system such the reduced crossed product $$A\rtimes _{r,\alpha } G$$ ⋊ r...

A method for the analytical enumeration of circulant graphs with p2 vertices, p a prime, is proposed and described in detail. It is based on the use of S-rings and P olya's enumeration technique. Two di erent approaches, \structural" and \multiplier", are developed and compared. As a result we get counting formulae and generating functions (by valency) for non-isomorphic p2-vertex directed and ...

This paper presents a hybridized formulation for the weak Galerkin finite element method for the biharmonic equation based on the discrete weak Hessian recently proposed by the authors. The hybridized weak Galerkin scheme is based on the use of a Lagrange multiplier defined on the element interfaces. The Lagrange multiplier is verified to provide a numerical approximation for certain derivative...