Related papers: On algebras that almost have finite dimensional re…
A notion of Drinfeld polynomials is introduced for modules of two-parameter quantum affine algebras. Finite dimensional representations are then characterized by sets of $l$-tuples of pairs of Drinfeld polynomials with certain conditions.
For a large class of finite W algebras, the defining relations of a Yangian are proved to be satisfied. Therefore such finite W algebras appear as realisations of Yangians. This result is useful to determine properties of such W algebra…
The set of linear, differential operators preserving the vector space of couples of polynomials of degrees n and n-2 in one real variable leads to an abstract associative graded algebra A(2). The irreducible, finite dimensional…
The residual finite-dimensionality of a $\mathrm{C}^*$-algebra is known to be encoded in a topological property of its space of representations, stating that finite-dimensional representations should be dense therein. We extend this…
We complete the classification of the finite dimensional irreducible representations of finite W-algebras associated to even multiplicity nilpotent elements in classical Lie algebras. This extends earlier work where this classification is…
We discuss a universal algebraic approach to quasi-exactly solvable models which allows us to interpret them as constrained Hamiltonian systems with a finite number of physical states. Using this approach we reproduce well-known…
The spatiality of derivations of quasi *-algebras is investigated by means of representation theory. Moreover, in view of physical applications, the spatiality of the limit of a family of spatial derivations is considered.
Motivated by the theory of graph limits, we introduce and study the convergence and limits of linear representations of finite groups over finite fields. The limit objects are infinite dimensional representations of free groups in…
In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.
We characterize finite-dimensional Lie algebras over an arbitrary field of characteristic zero which admit a non-trivial (quasi-) triangular Lie bialgebra structure.
In the paper the main attention is paid to conditions on algebras from a given variety which provide coincidence of their algebraic geometries. The main part here play the notions mentioned in the title of the paper.
For a couple of associative algebras we define the notion of their double and give a set of examples. Also, we discuss applications of such doubles to representation theory of certain quantum algebras and to a new type of Noncommutative…
We classify fields having finitely many finite non-commutative (not necessarily central) division algebras over them. In the process, we introduce the notion of anti-closure of a field and also make comments on fields having a linear…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
Nuclear $C^*$-algebras having a system of completely positive approximations formed with convex combinations of a uniformly bounded number of order zero summands are shown to be approximately finite dimensional.
The class of finitely presented algebras over a field $K$ with a set of generators $a_{1},..., a_{n}$ and defined by homogeneous relations of the form $a_{1}a_{2}... a_{n} =a_{\sigma (a)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…
We show how any finite-dimensional algebra can be realized as an idempotent subquotient of some symmetric quasi-hereditary algebra. In the special case of rigid symmetric algebras we show that they can be realized as centralizer subalgebras…
Establishing whether an algebra is quasi-hereditary or not is, in general, a difficult problem. In this paper we introduce a sufficient criterion to determine whether a general finite dimensional algebra is quasi-hereditary by showing that…
We show that semi-infinite cohomology of a finite dimensional graded algebra (satisfying some additional requirements) are a particular case of a general categorical construction. The motivating example is provided by small quantum groups…
In this note we study associative dialgebras proving that the most interesting such structures arise precisely when the algebra is not semiprime. In fact the presence of some "perfection" property (simpleness, primitiveness, primeness or…