Denote by Σn and Qn the set of all n × symmetric skew-symmetric matrices over a field $\mathbb {F}$ , respectively, where $\text {char}(\mathbb {F})\neq 2$ $|\mathbb {F}| \geq n^{2}+1$ . A characterization $\phi ,\psi :{\varSigma }_{n} \rightarrow {\varSigma }_{n}$ for which at least one them is surjective, satisfying $ \det (\phi (x)+\psi (y))=\det (x+y)\qquad (x,y\in }_{n}) given. Furthermore...

We consider a finite group acting on a vector space and the corresponding skew group algebra generated by the group and the symmetric algebra of the space. This skew group algebra illuminates the resulting orbifold and serves as a replacement for the ring of invariant polynomials, especially in the eyes of cohomology. One analyzes the Hochschild cohomology of the skew group algebra using isomor...

The classical Littlewood-Richardson rule is a rule for computing coefficients in many areas, and comes in many guises. In this paper we prove two Littlewood-Richardson rules for symmetric skew quasisymmetric Schur functions that are analogous to the famed version of the classical Littlewood-Richardson rule involving Yamanouchi words. Furthermore, both our rules contain this classical Littlewood...

In this paper we introduce two symmetric variants of amenability, symmetric module amenability and symmetric Connes amenability. We determine symmetric module amenability and symmetric Connes amenability of some concrete Banach algebras. Indeed, it is shown that $ell^1(S)$ is  a symmetric $ell^1(E)$-module amenable if and only if $S$ is amenable, where $S$ is an inverse semigroup with subsemigr...

We prove that semialgebraic sets of rectangular matrices a fixed rank, skew-symmetric rank and real symmetric whose eigenvalues have prescribed multiplicities are minimal submanifolds the space given size.

A square matrix is principally unimodular if every principal submatrix has determinant 0 or 1. Let A be a symmetric (0; 1)-matrix, with a zero diagonal. A PU-orientation of A is a skew-symmetric signing of A that is PU. If A 0 is a PU-orientation of A, then, by a certain decomposition of A, we can construct every PU-orientation of A from A 0. This construction is based on the fact that the PU-o...

We generalize the notion of Lagrangian subspaces to self-orthogonal subspaces with respect to a (skew-)symmetric form, thus characterizing (skew-) self-adjoint and unitary operators by means of self-orthogonal subspaces. By orthogonality preserving mappings, these characterizations can be transferred to abstract boundary value spaces of (skew-)symmetric operators. Introducing the notion of boun...

The theme of this paper is the construction of finite-difference approximations to the first derivative in the presence of Dirichlet boundary conditions. Stable implementation of splitting-based discretisation methods for the convectiondiffusion equation requires the underlying matrix to be skew symmetric and this turns out to be a surprisingly restrictive condition. We prove that no skewsymmet...