in this paper we consider selberg-type square matrices integrals with focus on kummer-beta types i & ii integrals. for generality of the results for real normed division algebras, the generalized matrix variate kummer-beta types i & ii are defined under the abstract algebra. then selberg-type integrals are calculated under orthogonal transformations.

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...

We show that the vertex algebra W1+∞ with central charge −1 is isomorphic to a tensor product of the simple W3 algebra with central charge −2 and a Heisenberg vertex algebra generated by a free bosonic field. We construct a family of irreducible modules of the W3 algebra with central charge −2 in terms of free fields and calculate the full character formulas of these modules with respect to the...

A classic result of representation theory is Brauer’s construction of a diagrammatical (geometrical) algebra whose matrix representation is a certain given matrix algebra, which is the commutating algebra of the enveloping algebra of the representation of the orthogonal group. The purpose of this paper is to provide a motivation for this result through the categorial notion of symmetric self-ad...

We prove that every positive trace on a countably generated ∗-algebra can be approximated by positive traces on algebras of generic matrices. This implies that every countably generated tracial ∗-algebra can be embedded into a metric ultraproduct of generic matrix algebras. As a particular consequence, every finite von Neumann algebra with separable pre-dual can be embedded into an ultraproduct...

Given a left module U and a right modules V over an algebra D and a bilinear form β : U × V → D, we may define an associative algebra structure on the tensor product V ⊗D U . This algebra is called a near-matrix algebra. In this paper, we shall investigate algebras filtered by near-matrix algebras in some nice way and give a unified treatment for quasi-hereditary algebras, cellular algebras, an...

In this paper we discuss matrix decompositions in the symmetrized max-plus algebra. The max-plus algebra has maximization and addition as basic operations. In contrast to linear algebra many fundamental problems in the max-plus algebra still have to be solved. In this paper we discuss max-algebraic analogues of some basic matrix decompositions from linear algebra. We show that we can use algori...

According to Frege’s principle the denotation of a sentence coincides with its truthvalue. The principle is investigated within the context of abstract algebraic logic, and it is shown that taken together with the deduction theorem it characterizes intuitionistic logic in a certain strong sense. A 2nd-order matrix is an algebra together with an algebraic closed set system on its universe. A ded...

We prove in this paper that the elliptic R–matrix of the eight vertex free fermion model is the intertwiner R–matrix of a quantum deformed Clifford–Hopf algebra. This algebra is constructed by affinization of a quantum Hopf deformation of the Clifford algebra. IMAFF-2/93 February 1993

As nowadays Machine Learning (ML) techniques are generating huge data collections, the problem of how to efficiently engineer their storage and operations is becoming paramount importance. In this article we propose a new lossless compression scheme for real-valued matrices which achieves efficient performance in terms ratio time linear-algebra operations. Experiments show that, as compressor, ...