Related papers: Algebras of infinite qubit systems
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
In this article the infinite product of bicomplex numbers is defined and the convergence and divergence of this product are discussed.
Over an algebraically closed field we classify all minimal representation-infinite algebras where the lattice of two-sided ideals is not distributive. As a consequence there are only finitely many isomorphism classes of minimal…
The application of the max-algebra to describe queueing systems by both linear scalar and vector equations is discussed. It is shown that these equations may be handled using ordinary algebraic manipulations. Examples of solving the…
We introduce invariant algebras and representation$^{(c_1,..., c_8)}$ of algebras, and give many ways of constructing Lie algebras, Jordan algebras, Leibniz algebras, pre-Lie algebras and left-symmetric algebras in an invariant algebras.
We construct some new Integrable Systems (IS) both classical and quantum associated with elliptic algebras. Our constructions are partly based on the algebraic integrability mechanism given by the existence of commuting families in skew…
We review some of the recent developments in two dimensional statistical mechanics in which corner transfer matrices provide the vital link between the physical system and the representation theory of quantum affine algebras. This opens…
Mathematical core of quantum mechanics is the theory of unitary representations of symmetries of physical systems. We argue that quantum behavior is a natural result of extraction of "observable" information about systems containing…
The problem of quantizing theories defined over configuration spaces described by non-commuting parameters is considered. In this paper we describe the first step in this direction, that is the definition of an integral over a general…
In this paper we prove that there exist infinitely many integers which can be expressed as a sum of four cubes of polynomials with integer coefficients. We give several identities that express the integers 1 and 2 as a sum of four cubes of…
Hopf algebra structures on the extended q-superplane and its differential algebra are defined. An algebra of forms which are obtained from the generators of the extended q-superplane is introduced and its Hopf algebra structure is given
Genetic and evolution algebras arise naturally from applied probability and stochastic processes. Gibbs measures describe interacting systems commonly studied in thermodynamics and statistical mechanics with applications in several fields.…
In this note, we derive a finite summation formula and an infinite summation formula involving Harmonic numbers of order up to some order by means of several definite integrals
Section headings: 1 Qubits, gates and networks 2 Quantum arithmetic and function evaluations 3 Algorithms and their complexity 4 From interferometers to computers 5 The first quantum algorithms 6 Quantum search 7 Optimal phase estimation 8…
We consider $m$-cluster tilted algebras arising from quivers of Euclidean type and we give necessary and sufficient conditions for those algebras to be representation finite. For the case $\widetilde{A}$, using the geometric realization, we…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…
Lie groups and quantum algebras are connected through their common universal enveloping algebra. The adjoint action of Lie group on its algebra is naturally extended to related q-algebra and q-coalgebra. In such a way, quantum structure can…
Coalgebras generalize various kinds of dynamical systems occuring in mathematics and computer science. Examples of systems that can be modeled as coalgebras include automata and Markov chains. We will present a coalgebraic representation of…
This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…
The goal of this paper is to consider some relations between varieties of representations of groups and varieties of associative algebras. The main emphasis is put on the varieties of representations of groups induced by the varieties of…