We generalise group algebras to other algebraic objects with bounded Hilbert space representation theory the generalised group algebras are called “host” algebras. The main property of a host algebra, is that its representation theory should be isomorphic (in the sense of the Gelfand–Raikov theorem) to a specified subset of representations of the algebraic object. Here we obtain both existence ...

The article proves topological representations for some classes of double Boolean algebras (dBas). In particular, representation theorems characterising fully contextual and pure dBas are obtained. Duality results also established.

This paper is devoted to the generalization of construction a Jordan algebra Lie and known theorems on local finite-dimensionality PI-algebras with an algebraic adjoint representation Mal’tsev algebras.

Knowledge representation is a popular research field in IT. As mathematical knowledge is most formalized, its representation is important and interesting. Mathematical knowledge consists of various mathematical theories. In this paper we consider a deductive system that derives mathematical notions, axioms and theorems. All these notions, axioms and theorems can be considered a small mathematic...

In this paper, it is our goal to develop the concept of Fourier transforms by using Representation Theory. We begin by laying basic definitions that will help us understand the definition of a representation of a group. Then, we define representations and provide useful definitions and theorems. We study representations and key theorems about representations such as Schur’s Lemma. In addition, ...

We propose a new type of quantum computer which is used to prove a spectral representation for a class S of computable sets. When S ∈ S codes the theorems of a formal system, the quantum computer produces through measurement all theorems and proofs of the formal system. We conjecture that the spectral representation is valid for all computably enumerable sets. The conjecture implies that the th...

Proof reuse addresses the issue of how proofs of theorems in a specific setting can be used to prove other theorems in different settings. This paper proposes an approach where theorems are generalised by abstracting their proofs from the original setting. The approach is based on a representation of proofs as logical framework proof terms, using the theorem prover Isabelle. The logical framewo...

Abstract Let F be a CM number field. We generalise existing automorphy lifting theorems for regular residually irreducible p -adic Galois representations over by relaxing the big image assumption on residual representation.

In this paper, our purpose is twofold. Firstly, the tensor andresiduum operations on $L-$nested systems are introduced under thecondition of complete residuated lattice. Then we show that$L-$nested systems form a complete residuated lattice, which isprecisely the classical isomorphic object of complete residuatedpower set lattice. Thus the new representation theorem of$L-$subsets on complete re...