Related papers: Mixed multiquadratic splitting fields

A field algebra is a ``non-commutative'' generalization of a vertex algebra. In this paper we develop foundations of the theory of field algebras.

We introduce the notions of mixed resolutions and simplicial sections, and prove a theorem relating them. This result is used (in another paper) to study deformation quantization in algebraic geometry.

Let $L$ be a separable quadratic extension of either $\mathbb{Q}$ or $\mathbb{F}_q(t)$. We propose efficient algorithms for finding isomorphisms between quaternion algebras over $L$. Our techniques are based on computing maximal one-sided…

We investigate finite field extensions of the unital 3-field, consisting of the unit element alone, and find considerable differences to classical field theory. Furthermore, the structure of their automorphism groups is clarified and the…

In this short note, we give a new sufficient condition for a linear map from a product of copies of a field to endomorphisms of a finite dimensional vector space over the same field to be an algebra homomorphism. We expect that this result…

In this paper we obtain a complete list of imaginary $n$-quadratic fields with class groups of exponent $3$ and $5$ under ERH for every positive integer $n$ where an $n$-quadratic field is a number field of degree $2^n$ represented as the…

We study a generalization of the classical correspondence between homogeneous quadratic polynomials, quadratic forms, and symmetric/alternating bilinear forms to forms in $n$ variables. The main tool is combinatorial polarization, and the…

This paper provides two characterizations of the primitive roots of unity in quadratic cyclotomic extensions over arbitrary fields. Firstly, we introduce a mapping from $\mathbb{N}$ to $\mathbb{N}$ crucial for describing these roots,…

Let $G$ be an algebraic group, $X$ a generically free $G$-variety, and $K=k(X)^G$. A field extension $L$ of $K$ is called a splitting field of $X$ if the image of the class of $X$ under the natural map $H^1(K, G) \mapsto H^1(L, G)$ is…

In the previous article we introduced the new concept of mixed representations of quivers and described the generators of their algebras of invariants. In this article we describe the defining relations of these algebras. Some applications…

For any integer $k\ge 1$, we show that there are infinitely many complex quadratic fields whose 2-class groups are cyclic of order $2^k$. The proof combines the circle method with an algebraic criterion for a complex quadratic ideal class…

The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…

The projection construction has been used to construct semifields of odd characteristic using a field and a twisted semifield [Commutative semifields from projection mappings, Designs, Codes and Cryptography, 61 (2011), 187--196]. We…

We investigate the structure of maximal commutative subalgebras of the finite dimensional Grassmann algebra over a field of characteristic different from two.

In this work we present different results concerning mixing properties of multivariate infinitely divisible (ID) stationary random fields. First, we derive some necessary and sufficient conditions for mixing of stationary ID multivariate…

We give an algebraic characterization of half-factorial orders in algebraic number fields. This generalizes prior results for seminormal orders and for orders in quadratic number fields.

We classify the rank two commutative semifields which are 8-dimensional over their center $\mathbb{F}_{q}$. This is done using computational methods utilizing the connection to linear sets in $\mathrm{PG}(2,q^{4})$. We then apply our…

Let $A$ be a finite dimensional algebra of finite global dimension over a finite field. In the present paper, we introduce certain elements in Bridgeland's Hall algebra of $A$, and give a multiplication theorem of these elements. In…

Let $F$ be a non-Archimedian local field of characteristic zero and $E/F$ a quadratic extension. The aim of the present article is to study the multiplicity of an irreducible admissible representation of ${\rm GL}_2(F)$ occurring in an…

We study quadratic approximations for two families of hyperquadratic continued fractions in the field of Laurent series over a finite field. As the first application, we give the answer to a question of the second author concerning…