相关论文: Quadratic descent of hermitian forms (with an erra…

A general scheme for determining and studying integrable deformations of algebraic curves is presented. The method is illustrated with the analysis of the hyperelliptic case. An associated multi-Hamiltonian hierarchy of systems of…

Properties of Hermitian forms are used to investigate several natural questions from CR Geometry. To each Hermitian symmetric polynomial we assign a Hermitian form. We study how the signature pairs of two Hermitian forms behave under the…

We give two congruence properties of Hermitian modular forms of degree 2 over $\mathbb{Q}(\sqrt{-1})$ and $\mathbb{Q}(\sqrt{-3})$. The one is a congruence criterion for Hermitian modular forms which is generalization of Sturm's theorem.…

Within the framework of the theory of the column and row determinants, we obtain determinantal representations of the Drazin inverse for Hermitian matrix over the quaternion skew field. Using the obtained determinantal representations of…

To an orthogonal or unitary involution on a central simple algebra of degree 4, or to a symplectic involution on a central simple algebra of degree 8, we associate a Pfister form that characterises the decomposability of the algebra with…

The paper discusses progress in understanding statistical properties of complex eigenvalues (and corresponding eigenvectors) of weakly non-unitary and non-Hermitian random matrices. Ensembles of this type emerge in various physical…

We describe all Witt invariants of anti-hermitian forms over a quaternion algebra with its canonical involution, and in particular all Witt invariants of orthogonal groups $O(A,\sigma)$ where $(A,\sigma)$ is an central simple algebra with…

Let R be a ring. A construction method for flexible quadratic algebras with scalar involution over R is presented which unifies various classical constructions in the literature, in particular those to construct composition algebras.

We investigate several classes of submanifolds of almost quaternionic skew-Hermitian manifolds $(M^{4n}, Q, \omega)$, including almost symplectic, almost complex, almost pseudo-Hermitian and almost quaternionic submanifolds. In the…

In these lectures we give an introduction to the reduction theory of binary forms starting with quadratic forms with real coefficients, Hermitian forms, and then define the Julia quadratic for any degree $n$ binary form. A survey of a…

We introduce the notion of maximal orders over quaternion algebras with orthogonal involution and give a classification over local fields, and a partial classification over algebraic number fields.

There are three types of involutions on a cubic fourfold; two of anti-symplectic type, and one symplectic. Here we show that cubics with involutions exhibit the full range of behaviour in relation to rationality conjectures. Namely, we show…

Let k be a commutative ring in which 2 is invertible. We prove that the Hermitian K-theory of quadric hypersurfaces over k admits fibration sequences relating it to the base ring and to Clifford algebras equipped with various duality…

In this article we study the involutions of $\mathrm{O}(V,\mathrm{q})$, an orthogonal group for a vector space $V$ with quadratic form $\mathrm{q}$ over a field of characteristic 2. The classification proceeds by discussing conjugacy…

In the case of quadratic forms over a field, it is well-known that the prime spectrum of the Witt ring and the space of orderings of the field determine one another, through associated signature maps. We show that a sililar relation holds…

Conjugation covariants of matrices are applied to study the real algebraic variety consisting of complex Hermitian matrices with a bounded number of distinct eigenvalues. A minimal generating system of the vanishing ideal of degenerate…

Solution and analysis of mathematical programming problems may be simplified when these problems are symmetric under appropriate linear transformations. In particular, a knowledge of the symmetries may help reduce the problem dimension, cut…

We study the intrinsic torsion of almost quaternion-Hermitian manifolds via the exterior algebra. In particular, we show how it is determined by particular three-forms formed from simple combinations of the exterior derivatives of the local…

This paper has two objectives. First, we study lattices with skew-Hermitian forms over division algebras with positive involutions. For division algebras of Albert types I and II, we show that such a lattice contains an "orthogonal" basis…

We devise a method that reduces the problem of classifying systems of forms and linear mappings to the problem of classifying systems of linear mappings. Canonical matrices of (i) bilinear or sesquilinear forms, (ii) pairs of symmetric,…