Related papers: Tressl's Structure Theorem for Separable Algebras
We give an efficient algorithm for Lang's Theorem in split connected reductive groups defined over finite fields of characteristic greater than 3. This algorithm can be used to construct many important structures in finite groups of Lie…
A cell algebra structure is found for a family of generalized Schur algebras previously studied by the author. This cell algebra structure is then used to construct the irreducible representations of these algebras and to determine when the…
We present a unified apoach to the study of separable and Frobenius algebras. The crucial observation is thsat both cases are related to the nonlinear equation $R^{12}R^{23}=R^{23}R^{13}=R^{13}R^{12}$, called the FS-equation. Given a…
The aim of this work is to investigate the structure of some skew twisted algebras, when the coefficient ring is a localization of the polynomial ring over the field of characteristic zero, and an involution is provided. A parallel…
We develop structure theory of finite Lie conformal superalgebras.
Using Y.Andr\'e's result on differential equations staisfied by $E$-functions, we derive an improved version of the Siegel-Shidlovskii theorem. It gives a complete characterisation of algebraic relations over the algebraic numbers between…
As a fundamental notion, the free differential algebra on a set is concretely constructed as the polynomial algebra on the differential variables. Such a construction is not known for the more general notion of the free differential algebra…
A differential algebra of finite type over a field k is a filtered algebra A, such that the associated graded algebra is finite over its center, and the center is a finitely generated k-algebra. The prototypical example is the algebra of…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
This is an addendum to the paper ``Deformation of $L_\infty$-Algebras'' of the same author. We explain in which way the deformation theory of $L_\infty$-algebras extends the deformation theory of singularities. We show that the construction…
Semifields are semirings in which every nonzero element has a multiplicative inverse. A rough classification uses the characteristic of the semifield, that is the isomorphism type of the semifield generated by the two neutral elements. For…
We prove a structure theorem for Yetter-Drinfel'd Hopf algebras over groups of prime order that are nontrivial, cocommutative, and cosemisimple: Under certain assumptions on the base field, these algebras can be decomposed into a tensor…
We discuss the differential graded Lie algebra (DGLA) of Drinfeld modeled on the tensor algebra of the universal enveloping algebra of a Lie algebra g over any field K of characteristic zero. We explicitly analyze the first obstruction to…
We prove a generalizations of the Elekes-Szab\'o theorem for relations definable in strongly minimal structures that are interpretable in distal structures.
The main aim of this paper is to classify the distinct multiplicative Lie algebra structures (up to isomorphism) on a given group. We also see that for a given group $G$, every homomorphism from the non-abelian exterior square $G \wedge G$…
A graded-division algebra is an algebra graded by a group such that all nonzero homogeneous elements are invertible. This includes division algebras equipped with an arbitrary group grading (including the trivial grading). We show that a…
We develop an obstruction theory for Hirsch extensions of cbba's with twisted coefficients. This leads to a variety of applications, including a structural theorem for minimal cbba's, a construction of relative minimal models with twisted…
We classify 0-dimensional spectral triples over complex and real algebras and provide some general statements about their differential structure. We investigate also whether such spectral triples admit a symmetry arising from the Hopf…
The theory of abstract kernels in non-trivial extensions for many kinds of algebraical objects, such as groups, rings and graded rings, associative algebras, Lie algebras, restricted Lie algebras, DG-algebras and DG-Lie algebras, has been…
Answering a question of J.~Kovacic, we show that, for any Keigher ring, its differential spectrum coincides with the differential spectrum of the ring of global sections of the structure sheaf. In particular, we obtain the answer for Ritt…