Related papers: Algebras of infinite qubit systems
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
In this article, we give two examples of finitely presented quadratic algebras (algebras presented by quadratic relations) of intermediate growth.
In the paper is discussed complete probabilistic description of quantum systems with application to multiqubit quantum computations. In simplest case it is a set of probabilities of transitions to some fixed set of states. The probabilities…
This is a survey on stated skein algebras and their representations.
These notes collect results about algebraic correspondences and adapt them to the setting of correspondences on projective lines. The focus lies on finite orbits of algebraic correspondences. The main result is a field theoretic…
Infinite dimensional representations of the real form U_q(u_{n,1}) of the Drinfeld--Jimbo algebra U_q(gl_{n+1}) are defined. The principal series of representations of U_q(u_{n,1}) is studied. Intertwining operators for pairs of the…
The operator algebra is introduced based on the framework of logarithmic representation of infinitesimal generators. In conclusion a set of generally-unbounded infinitesimal generators is characterized as a module over the Banach algebra.
A catalogue of explicit realizations of representations of (super) Lie algebras and quantum algebras in Fock space is presented.
A complete list of Uq(sl2)-module algebra structures on the quantum plane is produced and the (uncountable family of) isomorphism classes of these structures are described. The composition series of representations in question are computed.…
We investigate the cluster-tilted algebras of finite representation type over an algebraically closed field. We give an explicit description of the relations for the quivers for finite representation type. As a consequence we show that a…
We give a complete description of Lie algebras graded by an infinite irreducible locally finite root system.
Let k be a field. A finite dimensional k-algebra is said to be minimal representation-infinite provided it is representation-infinite and all its proper factor algebras are representation-finite. Our aim is to classify the special biserial…
Matrices are very popular and widely used in mathematics and other fields of science. Every mathematician has known the properties of finite-sized matrices since the time of study. In this paper, we consider the basic theory of infnite…
Finite versions of W-algebras are introduced by considering (symplectic) reductions of finite dimensional simple Lie algebras. In particular a finite analogue of $W^{(2)}_3$ is introduced and studied in detail. Its unitary and non-unitary,…
In this article we review the basic concepts regarding quantum integrability. Special emphasis is given on the algebraic content of integrable models. The associated algebras are essentially described by the Yang-Baxter and boundary…
Finite and Infinite-dimensional representations of symmetry algebras play a significant role in determining the spectral properties of physical Hamiltonians. In this paper, we introduce and apply a practical method to construct infinite…
We study endomorphisms and derivations of infinite dimensional cyclic Leibniz algebra.
We describe the finite-dimensional simple modules of all the (twisted and untwisted) multiloop algebras and classify them up to isomorphism.
We introduce quantum Boolean algebras which are the analogue of the Weyl algebras for Boolean affine spaces. We study quantum Boolean algebras from the logical and set theoretical viewpoints.
We study finite dimensional algebras that appear as fibers of quantum orders over a given point of variety of center. We present the formula for the number of irreducible representations and check it for it for the algebra of twisted…