Related papers: Combinatorial geometries of field extensions
In the paper we give a complete classification of $2$-dimensional evolution algebras over algebraically closed fields, describe their groups of automorphisms and derivation algebras.
We study groups definable in existentially closed geometric fields with commuting derivations. Our main result is that such a group can be definably embedded in a group interpretable in the underlying geometric field. Compared to earlier…
We give an elementary construction of an arbitrary differentially closed field and of a universal differential extension of a differential field in terms of Nash function fields. We also give a characterization of any Archimedean ordered…
This paper focuses on the derivations and automorphism groups of certain finite-dimensional associative algebras over the field of complex numbers. Using classification results for algebras of dimensions two, three, and four, along with…
The space of derivations of finite dimensional evolution algebras associated to graphs over a field with characteristic zero has been completely characterized in the literature. In this work we generalize that characterization by describing…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…
We define two classes of topological infinite degree covering maps modeled on two families of transcendental holomorphic maps. The first, which we call exponential maps of type $(p,q)$, are branched covers and is modeled on transcendental…
We describe arbitrary multiplicative differential forms on Lie groupoids infinitesimally, i.e., in terms of Lie algebroid data. This description is based on the study of linear differential forms on Lie algebroids and encompasses many known…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.
We give a classification of maximal elements of the set of finite groups that can be realized as the automorphism groups of polarized abelian threefolds over finite fields.
Orthogonal spaces are vector spaces together with a quadratic form whose associated bilinear form is non-degenerate. Over fields of characteristic two, there are many quadratic forms associated to a given bilinear form and quadratic…
This is a survey on the automorphism groups in various classes of affine algebraic surfaces and the algebraic group actions on such surfaces. Being infinite-dimensional, these automorphism groups share some important features of algebraic…
We show that algebraic analogues of universal group covers, surjective group homomorphisms from a $\mathbb{Q}$-vector space to $F^{\times}$ with "standard kernel", are determined up to isomorphism of the algebraic structure by the…
In this paper we look into the structure of finite-dimensional graded superalgebras of various types such as associative, Lie and Jordan over an algebraically closed field of characteristic zero.
We present a complete computational classification of the combinatorial types of hyperplane sections, or slices, of the regular cube up to dimension six. For each dimension, we determine the exact number of distinct combinatorial types.…
In this note, we establish an equivalence of categories between the category of all eight-dimensional composition algebras with any given quadratic form $n$ over a field $k$ of characteristic not two, and a category arising from an action…
The paper contains a survey of train constructions for infinite symmetric groups and related groups. For certain pairs (a group $G$, a subgroup $K$), we construct categories, whose morphisms are two-dimensional surfaces tiled by polygons…
We prove the finiteness of the genus of finite-dimensional division algebras over many infinitely generated fields. More precisely, let $K$ be a finite field extension of a field which is a purely transcendental extension of infinite…
In this paper, we give a survey of the known results concerning the tensor rank of the multiplication in finite extensions of finite fields, enriched with some not published recent results as well as analyzes enhancing the qualitative…
Associated to any hypergraph is a toric ideal encoding the algebraic relations among its edges. We study these ideals and the combinatorics of their minimal generators, and derive general degree bounds for both uniform and non-uniform…