相关论文: Triple Representation Theorem for homogeneous effe…
A partial algebra construction of Gr\"atzer and Schmidt from "Characterizations of congruence lattices of abstract algebras" (Acta Sci. Math. (Szeged) 24 (1963), 34-59) is adapted to provide an alternative proof to a well-known fact that…
We present an algebraic approach for finding exact solutions of the wave equation. The approach, which is referred to as the Tridiagonal Representation Approach (TRA), is inspired by the J-matrix method and based on the theory of orthogonal…
We prove new Brown representability theorems for triangulated categories using metric techniques as introduced in the work of Neeman. In the setting of algebraic geometry, this gives us new representability theorems for homological and…
Effect algebras are a generalization of many structures which arise in quantum physics and in mathematical economics. We show that, in every modular Archimedean atomic lattice effect algebra $E$ that is not an orthomodular lattice there…
Ariki's and Grojnowski's approach to the representation theory of affine Hecke algebras of type $A$ is applied to type $B$ with unequal parameters to obtain -- under certain restrictions on the eigenvalues of the lattice operators --…
We prove a compactness and integral-representation theorem for sequences of families of lattice energies describing atomistic interactions defined on lattices with vanishing lattice spacing. The densities of these energies may depend on…
In this paper we define and study dimension generalized effect algebras (DGEAs), i.e., Dedekind orthocomplete and centrally orthocomplete generalized effect algebras equipped with a dimension equivalence relation. Our theory is a bona fide…
The aim of this paper is to give new representation theorems for extended contact algebras. These representation theorems are based on equivalence relations.
We prove that the interval topology of an Archimedean atomic lattice effect algebra $E$ is Hausdorff whenever the set of all atoms of $E$ is almost orthogonal. In such a case $E$ is order continuous. If moreover $E$ is complete then order…
We introduce the concept of a quasiresiduated lattice and prove that every lattice effect algebra can be organized into a commutative quasiresiduated lattice with divisibility. Also conversely, every such a lattice can be converted into a…
Let W be a finite Coxeter group. We define its Hecke-group algebra by gluing together appropriately its group algebra and its 0-Hecke algebra. We describe in detail this algebra (dimension, several bases, conjectural presentation,…
We study the question of when geometric extension algebras are polynomial quasihereditary. Our main theorem is that under certain assumptions, a geometric extension algebra is polynomial quasihereditary if and only if it arises from an even…
The purpose of this paper is to study representations of simple multiplicative Hom-Lie algebras. First, we provide a new proof using Killing form for characterization theorem of simple Hom-Lie algebras given by Chen and Han, then discuss…
The paper is the survey of the modern results and applications of the theory of homotopes. The notion of a well-tempered element in an associative algebra is introduced and it is proven that the category of representations of the homotope…
We characterize atomistic effect algebras, prove that a weakly orthocomplete Archimedean atomic effect algebra is orthoatomistic and present an example of an orthoatomistic orthomodular poset that is not weakly orthocomplete.
We use Reznick's Theorem for positive homogeneous polynomials to prove an elliptic regularity result for representations of enveloping algebras of Lie algebras. This allows us to relax a technical condition for a sum of squares…
We review some facts about the representation theory of the Hecke algebra. We adapt for the Hecke algebra case the approach of Okounkov and Vershik which was developed for the representation theory of symmetric groups. We justify an…
For representation by partial functions in the signature with intersection, composition and antidomain, we show that a representation is meet complete if and only if it is join complete. We show that a representation is complete if and only…
In this paper, first we introduce the notion of an omni-representation of a Leibniz algebra $\g$ on a vector space $V$ as a Leibniz algebra homomorphism from $\g$ to the omni-Lie algebra $\gl(V)\oplus V$. Then we introduce the…
We prove mean and pointwise ergodic theorems for the action of a discrete lattice subgroup in a connected algebraic Lie group, on infinite volume homogeneous algebraic varieties. Under suitable necessary conditions, our results are…