Definition 1.1. Let A be an involutive algebra over C with involution ξ 7→ ξ (resp. ξ 7→ ξ). We say A is a left (resp. right) Hilbert algebra if A has a inner product (· | ·) satisfying: a. Multiplication on the left (resp. right) is a bounded operator; that is, ∀ξ ∈ A the map πl(ξ) : η 7→ ξη (resp. πr(ξ) : η 7→ ηξ) is bounded on A. b. (ξη | ζ) = (η | ξζ) (resp. (ξη | ζ) = (ξ | ζη)). c. The inv...

We show that an orthogonal involution of a central division algebra D (over a field of characteristic not 2) remains anisotropic over the generic splitting field of D. We also give a couple of other applications of the same technique.

Let K be a field and P partially ordered set (poset). FI(P,K) I(P,K) the finitary incidence algebra space of over K, respectively, let D(P,K)=FI(P,K)⊕I(P,K) idealization FI(P,K)-bimodule I(P,K). In first part this paper, we show that D(P,K) has an anti-automorphism (involution) if only (involution). We also present characterization anti-automorphisms involutions on D(P,K). second part, obtain c...

We start this paper by showing that the Leavitt path algebra of a (row-finite) graph is an algebra of quotients of the corresponding path algebra. The path algebra is semiprime if and only if whenever there is a path connecting two vertices, there is another one in the opposite direction. Semiprimeness is studied because, for acyclic graphs, the Leavitt path algebra is a Fountain-Gould algebra ...

The field of neural networks has seen significant advances in recent years with the development deep and convolutional networks. Although many current works address real-valued models, studies reveal that hypercomplex-valued parameters can better capture, generalize, represent complexity multidimensional data. This paper explores quaternion-valued network application for a pattern recognition t...

Let Fq be a finite field of q elements, F a p-adic field and D is a quaternion division algebra over F . This paper proves uniqueness of Shalika models for GL2n(Fq) and GL2n(D), and re-obtain uniqueness of Shalika models for GL2n(F), 1 for any n ∈ N.

In this paper we will construct a lattice-based public-key cryptosystem using non-commutative quaternion algebra, and since its lattice does not fully fit within Circular and Convolutional Modular Lattice (CCML), we prove it is arguably more secure than the existing lattice-based cryptosystems such as NTRU. As in NTRU, the proposed public-key cryptosystem relies for its inherent securi...

Edge detection is widely used for image processing to improve the and classification of objects, segmentation, extraction other features. Satellite images are rich in information about objects with different color intensity have a large amount noise, so it difficult achieve recognition, classification, feature small through traditional edge algorithms. The colors satellite suffer from overlap d...

Quaternion is a four-dimensional and an extension of the complex number system. It often viewed from various fields, such as analysis, algebra, geometry. Several applications quaternions are related to object’s rotation motion in three-dimensional space form differential equation. In this paper, we do systematic literature review on development quaternion equations. We utilize PRISMA (preferred...