Related papers: Modular adjacency algebras of Dual polar schemes
We define modular Terwilliger algebras of association schemes, Terwilliger algebras over a positive characteristic field, and consider basic properties. We give a condition for the modular Terwilliger algebra to be non-semisimple. We show…
Two extension problems are solved. First, the class of locally matricial algebras over an arbitrary field is closed under extensions. Second, the class of locally finite dimensional semisimple algebras over a fixed field is closed under…
This paper is mainly devoted to a structure study of Hom-alternative algebras . Equivalent conditions for Hom-alternative algebras being solvable, simple and semi-simple are displayed. Moreover some results about Hom-alternative bimodule…
This paper is a further contribution to the extensive study by a number of authors of the subalgebra lattice of a Lie algebra. It is shown that, in certain circumstances, including for all solvable algebras, for all Lie algebras over…
A finite-dimensional unital and associative algebra over $\mathbb{R}$, or what we shall call simply "an algebra" in this paper for short, generalities the construction by which we derive the complex numbers by "adjoining an element $i$" to…
Algebras defined over fields of characteristic zero and positive characteristic usually do not behave the same way. However, for certain algebras, for example the group algebras, they behave the same way as the characteristic zero case at…
We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…
We investigate some properties of regularity of homomorphisms of local algebras over positive characteristic fields. We state a result of monomialization of such a homomorphism between algebras of analytic or algebraic power series. From…
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…
In this paper, we study local systems of locally finite associative algebras over fields of characteristic p\ge0. We describe the perfect local systems and study the relation between them and their corresponding locally finite associative…
This work introduces author's approach to harmonic analysis on algebraic groups over functional two-dimensional local fields. For a two-dimensional local field a Hecke algebra which is formed by operators which integrate…
We give a definition of associative schemes, schemes of associative rings, over a field $k,$ using the definition of completion of an associative $k$-algebra in a finite set of simple modules. We start by giving a weaker but sufficient…
Vertex algebras formalize the subalgebra of holomorphic fields of a conformal field theory. OPE-algebras were proposed as a generalization of vertex algebras that formalizes the algebra of all fields of a conformal field theory. We prove…
It is well known that the adjacency algebra of an association scheme has the standard character. In this paper we first define the concept of standard character for C-algebras and we say that a C-algebra has the {\it standard character…
Let $p$ denote a prime number. In this note, we focus on the modular Terwilliger algebras of association schemes defined in [3]. We define the primary module of a modular Terwilliger algebra of an association scheme and determine all its…
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…
For a Lie algebra L over an algebraically closed field of non-zero characteristic, every finite-dimensional L-module can be decomposed into a direct sum of submodules such that all composition factors of a summand have the same character.…
Classically, there are two model category structures on coalgebras in the category of chain complexes over a field. In one, the weak equivalences are maps which induce an isomorphism on homology. In the other, the weak equivalences are maps…
In this article we discuss the Hopf algebras spanned by the adjacency matrices in detail. We show that there two Hopf algebraic structures concerning the adjacency matrices, one is the copy of Connes-Kreimer Hopf algebra, another one is the…
A complete classifications, up to isomorphism, of two-dimensional associative and diassociative algebras over any basic field are given.