Related papers: Common Splitting Fields of Symbol Algebras

We discuss rather systematically the principle, implicit in earlier works, that for a "random" element in an arithmetic subgroup of a (split, say) reductive algebraic group over a number field, the splitting field of the characteristic…

To what extent does the maximal subfield spectrum of a division algebra determine the isomorphism class of that algebra? It has been shown that over some fields a quaternion division algebra's isomorphism class is largely if not entirely…

Let S be a symbol algebra. The trace form of S is computed and it is shown how this form can be used to determine whether S is a division algebra or not. In addition, the exterior powers of the trace form of S are computed.

Adjoining to the language of rings the function symbols for splitting coefficients, the function symbols for relative $p$-coordinate functions, and the division predicate for a valuation, some theories of pseudo-algebraically closed…

In this paper, we consider partially commutative metabelian Lie algebras whose defining graphs are cycles. We show that such algebras are universally equivalent iff the corresponding cycles have the same length. Moreover, we give an example…

To study the set of torsion classes of a finite dimensional basic algebra, we use a decomposition, called sign-decomposition, parametrized by elements of $\{\pm1\}^n$ where $n$ is the number of simple modules. If $A$ is an algebra with…

We introduce multi-colour partition algebras $P_{n,m}(\delta_0, ..., \delta_{m-1})$, which are generalization of both bubble algebras and partition algebras, then define the bubble algebra $T_{n,m}(\delta_0, ..., \delta_{m-1})$ as a…

This paper consists of variations upon the theme of limiting modular symbols. Topics covered are: an expression of limiting modular symbols as Birkhoff averages on level sets of the Lyapunov exponent of the shift of the continued fraction,…

Let $R$ be a finite-dimensional algebra over an algebraically closed field $F$ graded by an arbitrary group $G$. We prove that $R$ is a graded division algebra if and only if it is isomorphic to a twisted group algebra of some finite…

We compute the Hochschild, cyclic, and periodic cyclic homology groups of algebras of families of Laurent complete symbols on manifolds with corners. We show in particular that the spectral sequence associated with Hochschild homology…

The problem of efficiently characterizing degree sequences of simple hypergraphs is a fundamental long-standing open problem in Graph Theory. Several results are known for restricted versions of this problem. This paper adds to the list of…

For $m\in\mathbb{R}$ we introduce the symbol classes $S^m$, $m\in\mathbb{R}$, consisting of smooth functions $\sigma$ on $\mathbb{R}^{2d}$ such that $|\partial^\alpha \sigma(z)|\leq C_\alpha (1+|z|^2)^{m/2}$, $z\in\mathbb{R}^{2d}$, and we…

We revisit the famous theorem of Albert's on the cyclicity of tensor products of cyclic $p$-algebras. In the case of tensor products of cyclic $p$-algebras of prime degree, we provide an explicit computation of the resulting cyclic algebra…

A computably presented algebraic field $F$ has a \emph{splitting algorithm} if it is decidable which polynomials in $F[X]$ are irreducible there. We prove that such a field is computably categorical iff it is decidable which pairs of…

We introduce characteristic classes for the spectral sequence associated to a split short exact sequence of Hopf algebras. We show that these characteristic classes can be seen as obstructions for the vanishing of differentials in the…

The genus gen(D) of a finite-dimensional central division algebra D over a field F is defined as the collection of classes [D'] in the Brauer group Br(F), where D' is a central division F-algebra having the same maximal subfields as D. For…

We introduce the class of split regular Hom-Leibniz algebras as the natural generalization of split Leibniz algebras and split regular Hom-Lie algebras. By developing techniques of connections of roots for this kind of algebras, we show…

In this paper we study some special classes of division algebras over a Laurent series field with arbitrary residue field. We call the algebras from these classes as splittable and good splittable division algebras. It is shown that these…

Let F be a field of transcendence degree one over a p-adic field, and let l be a prime not equal to p. Results of Merkurjev and Saltman show that H^2(F,\mu_l) is generated by Z/l-cyclic classes. We prove the "Z/l-length" in H^2(F,\mu_l)…

In this paper we will study some properties of the matrix representations of symbol algebras of degree three, we study some equations with coefficients in these algebras, we find an octonion algebra in a symbol algebra of degree three, we…