Related papers: On minimal representation-infinite algebras
Given a finite connected bipartite graph, finite-dimensional indecomposable semisimple Leibniz algebras are constructed. Furthermore, any finite-dimensional indecomposable semisimple Leibniz algebra admits a similar construction.
By [R. Bautista, P. Gabriel, A.V Roiter., L. Salmeron, Representation-finite algebras and multiplicative basis. Invent. Math. 81 (1985) 217-285.], a finite-dimensional algebra having finitely many isoclasses of indecomposable…
We define a class of algebras describing links of binary semi-isolating formulas on a set of realizations for a family of 1-types of a complete theory. These algebras include algebras of isolating formulas considered before. We prove that a…
Many finite symmetric integral non-representable relation algebras, including almost all Monk algebras, can be embedded in the completion of an atomic symmetric integral representable relation algebra whose finitely-generated subalgebras…
It is well known that a finite-dimensional Lie algebra over a field of characteristic zero is simple exactly when its derivation algebra is simple. In this paper we characterize those Lie algebras of arbitrary dimension over any field that…
In this paper we study the possibility to define irreducible representations of the symmetric groups with the help of finitely many relations. The existence of finite bases is established for the classes of representations corresponding to…
We classify small binary bibraces, using the correspondence with alternating algebras over the field F2, up to dimension eight, also determining their isomorphism classes. These finite-dimensional algebras, defined by an alternating…
It is shown that, given any finite dimensional, split basic algebra $\Lambda = K\Gamma/I$ (where $\Gamma$ is a quiver and $I$ an admissible ideal in the path algebra $K \Gamma$), there is a finite list of affine algebraic varieties, the…
We classify (possibly non commutative) algebras of low rank over a domain R. We first review results for algebras of rank 2 and for finite-dimensional division algebras over the real numbers. These results motivate us to consider which…
We start with observing that the only connected finite dimensional algebras with finitely many isomorphism classes of indecomposable bimodules are the quotients of the path algebras of uniformly oriented $A_n$-quivers modulo the radical…
One of the longstanding problems in universal algebra is the question of which finite lattices are isomorphic to the congruence lattices of finite algebras. This question can be phrased as which finite lattices can be represented as…
Representable implication algebras are known to be axiomatised by a finite number of equations (making the representation and finite representation problems decidable here). We show that this also holds in the context of unary (and binary)…
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 paper we find minimal faithful representations of several classes filiform Lie algebras by means of strictly upper-triangular matrices. We investigate Leibniz algebras whose corresponding Lie algebras are filiform Lie algebras such…
The paper is devoted to classification problem of finite dimensional complex none Lie filiform Leibniz algebras. Actually, the observations show there are two resources to get classification of filiform Leibniz algebras. The first of them…
We classify essential algebras whose irredundant non-refinable covers consist of primal algebras. The proof is obtained by constructing one to one correspondence between such algebras and partial orders on finite sets. Further, we prove…
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We describe automorphisms and derivations of several important associative and Lie algebras of infinite matrices over a field.
Motivated by the theory of unitary representations of finite dimensional Lie supergroups, we describe those Lie superalgebras which have a faithful finite dimensional unitary representation. We call these Lie superalgebras unitary. This is…
We provide non-isomorphic finite 2-groups which have isomorphic group algebras over any field of characteristic 2, thus settling the Modular Isomorphism Problem.