相关论文: Pfister involutions

The u-invariant of a field is the supremum of the dimensions of anisotropic quadratic forms over the field. We define corresponding u-invariants for hermitian and generalised quadratic forms over a division algebra with involution in…

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.

Heisenberg groups over algebras with central involution and their automorphism groups are constructed. The complex quaternion group algebra over a prime field is used as an example. Its subspaces provide finite models for each of the real…

An involution is usually defined as a mapping that is its own inverse. In this paper, we study quaternion involutions that have the additional properties of distribution over addition and multiplication. We review formal axioms for such…

In this short note, we describe the so-called homogeneous involution on finite-dimensional graded-division algebra over an algebraically closed field. We also compute their graded polynomial identities with involution. As pointed out by L.…

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…

Contrary to the expected behavior, we show the existence of non-invertible deformations of Lie algebras which can generate invariants for the coadjoint representation, as well as delete cohomology with values in the trivial or adjoint…

We extend all cohomological invariants of similarity classes of quadratic forms to anti-hermitian forms over a quaternion algebra. This uses the fact that such invariants can be lifted to Witt invariants, which can be described as…

The problem of whether a metabolic idempotent of a central simple algebra with involution is contained in an invariant quaternion subalgebra is investigated. As an application, the similar problem is studied for skew-symmetric elements…

We introduce new polynomial invariants of a finite-dimensional semisimple and cosemisimple Hopf algebra A over a field by using the braiding structures of A. We investigate basic properties of the polynomial invariants including stability…

G. Prasad and A. Rapinchuk asked if two quaternion division F -algebras that have the same subfields are necessarily isomorphic. The answer is known to be "no" for some very large fields. We prove that the answer is "yes" if F is an…

We obtain some criteria for a symmetric square-central element of a totally decomposable algebra with orthogonal involution in characteristic two, to be contained in an invariant quaternion subalgebra.

The theory of algebras with polynomial identities has developed significantly, with special attention devoted to the classification of varieties according to the asymptotic behavior of their codimension sequences. This sequence is a…

Dendriform algebras are certain splitting of associative algebras and arise naturally from Rota-Baxter operators, shuffle algebras and planar binary trees. In this paper, we first consider involutive dendriform algebras, their cohomology…

We investigate Lie bialgebra structures on simple Lie algebras of non-split type $A$. It turns out that there are several classes of such Lie bialgebra structures, and it is possible to classify some of them. The classification is obtained…

Using the Rost invariant for non split simply connected groups, we define a relative degree $3$ cohomological invariant for pairs of orthogonal or unitary involutions having isomorphic Clifford or discriminant algebras. The main purpose of…

In this paper we study certain quaternion algebras and symbol algebras which split.

We associate an $(n_1+\dots+n_t-k(t-1))$-fold Pfister form to any $t$-tuple of $k$-linked Pfister forms of dimensions $2^{n_1},\dots,2^{n_t}$, and prove its invariance under the different symbol presentations of the forms with a common…

Let $k$ be an algebraically closed base field of characteristic zero. The category equivalence between central simple algebras and irreducible, generically free $PGL_n$-varieties is extended to the context of central simple algebras with…

We associate an square to any two dimensional evolution algebra. This geometric object is uniquely determined, does not depend on the basis and describes the structure and the behaviour of the algebra. We determine the identities of degrees…