Related papers: Isotropy of orthogonal involutions

Let S be an essentially smooth scheme over a field and l a prime number invertible on S. We show that the algebra of bistable operations in the mod l motivic cohomology of smooth S-schemes is generated by the motivic Steenrod operations.…

Let $R$ be a commutative and unital semi-local ring in which 2 is invertible. In this note, we show that anisotropic quadratic spaces over $R$ remain anisotropic after base change to any odd-degree finite \'{e}tale extension of $R$. This…

In this paper, we investigate subnormal subgroups of the multiplicative group of an almost locally simple artinian algebra with involution. In particular, we show that if either the set of traces or the set of norms of such a subgroup with…

We establish new and different kinds of proofs of properties that arise due to the orthogonal decomposition of the Hilbert space, including projections, over the unit interval of one dimension. We also see angles between functions,…

Symmetry algebras deriving from towers of soft theorems can be deformed by a short list of higher-dimension Wilsonian corrections to the effective action. We study the simplest of these deformations in gauge theory arising from a massless…

It is shown that rational extensions of the isotropic Dunkl oscillator in the plane can be obtained by adding some terms either to the radial equation or to the angular one obtained in the polar coordinates approach. In the former case, the…

The aim of this paper is to revisit the question of local-global principles for embeddings of \'etale algebras with involution into central simple algebras with involution over global fields of characteristic not 2. A necessary and…

We show that any accordion complex associated to a dissection of a convex polygon is isomorphic to the support $\tau$-tilting simplicial complex of an explicit finite dimensional algebra. To this end, we prove a property of some induced…

Coisotropic algebras consist of triples of algebras for which a reduction can be defined and unify in a very algebraic fashion coisotropic reduction in several settings. In this paper we study the theory of (formal) deformation of…

We consider an anisotropic L\'evy operator $\mathcal{I}_s$ of any order $s\in(0,1)$ and we consider the homogenization properties of an evolution equation. The scaling properties and the effective Hamiltonian that we obtain is different…

The hermitian u-invariants of a central simple algebra with involution are studied. In this context, a new technique is obtained to give bounds for the behavior of these invariants under a quadratic field extension. This is applied to…

We consider proper, algebraic semismall maps f from a complex algebraic manifold X. We show that the topological Decomposition Theorem implies a "motivic" decomposition theorem for the rational algebraic cycles of X and, in the case X is…

In this paper we construct new derived invariants with integral coefficients using the theory of motifs, and give several applications. Specifically, we obtain the following results: For complex algebraic surfaces, we prove that certain…

We give necessary and sufficient conditions for a family of inner products in a finite-dimensional vector space $V$ over an arbitrary field $\mathbb{K}$ to have an orthogonal basis relative to all the inner products. Some applications to…

The affine group scheme of automorphisms of an evolution algebra that is equal to its square, is shown to lie in an exact sequence, such that the other terms depend solely on the directed graph associated to the algebra. As a consequence,…

A deterministic application $\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}^2$ deforms bijectively and regularly the plane and allows to build a deformed random field $X\circ\theta\,:\,\mathbb{R}^2\rightarrow\mathbb{R}$ from a regular,…

Orthogonal polynomials on quadratic curves in the plane are studied. These include orthogonal polynomials on ellipses, parabolas, hyperbolas, and two lines. For an integral with respect to an appropriate weight function defined on any…

Let $k$ be a field of odd prime characteristic $p$. We calculate the Lie algebra structure of the first Hochschild cohomology of a class of quantum complete intersections over $k$. As a consequence, we prove that if $B$ is a defect…

In this note we are going to consider a smooth projective surface equipped with an involution and study the action of the involution at the level of Chow group of zero cycles.

This paper deals with the classification of Leibniz central extensions of a naturally graded filiform Lie algebra. We choose a basis with respect to that the table of multiplication has a simple form. In low dimensional cases isomorphism…