Related papers: Representation theory and an isomorphism theorem f…
We show that, also within the class of representation-tame finite dimensional algebras $\Lambda$, the big left finitistic dimension of $\Lambda$ may be strictly larger than the little. In fact, the discrepancies $Findim \Lambda - findim…
We study irreducible modules for Toroidal Lie-algebras with finite dimensional weight spaces. First note that Toroidal Lie-algebras have infinite dimensional center. In genaral the infinite dimensional center does not act as scalars on an…
Bihom-Lie algebra is a generalized Hom-Lie algebra endowed with two commuting multiplicative linear maps. In this paper, we study cohomology and representations of Bihom-Lie algebras. In particular, derivations, central extensions,…
Suppose B is the unital algebra consisting of the algebraic product of full matrix algebras over an index set X. A bijection is set up between the equivalence classes of irreducible representations of B as operators on a Banach space and…
Cohen and Taylor introduced Plesken Lie algebra as certain Lie algebra constructed using finite groups. Arjun and Romeo described the linear representation of these Lie algebras induced from group representation in [1]. Hence the authors…
We give an historical survey of some of the original basic algebraic and combinatorial results on Temperley-Lieb algebras, with a focus on certain results that have become folklore.
A class of representations of a Lie superalgebra (over a commutative superring) in its symmetric algebra is studied. As an application we get a direct and natural proof of a strong form of the Poincare'-Birkhoff-Witt theorem, extending this…
We say that there is a representation of the universal algebra B in the universal algebra A if the set of endomorphisms of the universal algebra A has the structure of universal algebra B. Therefore, the role of representation of the…
The Lie algebra $gl(V)$ is the Lie algebra of all endomorphisms of a countable-dimensional complex vector space $V$. We define a tensor category of topological representations of the Lie algebra $gl(V)$, so that $V$, its dual and the…
In this paper we show that for a $n$-Filippov algebra $\g,$ the tensor power $\g^{\otimes n-1}$ is endowed with a structure of anti-symmetric co-representation over the Leibniz algebra $\g^{\wedge n-1}$. This co-representation is used to…
Let $n$ be a nonnegative integer, we use ribbon $n-$graph diagrams and the Yamada polynomial skein relations to construct an algebra ${\mathcal Y}_n$ which is shown to be closely related to the Temerley-Lieb Algebra. We prove that the…
We give a simplified complete proof for the classification of the selfinjective representation-finite algebras of finite dimension over an algebraically closed field. We explain the relations between the two different approaches and also to…
From the viewpoint of higher dimensional Auslander-Reiten theory, we introduce a new class of finite dimensional algebras of global dimension n, which we call n-representation infinite. They are a certain analog of representation infinite…
In this article we introduce a framization of the Hecke algebra of type B. For this framization we construct a faithful tensorial representation and two linear bases. We finally construct a Markov trace on these algebras and from this trace…
In this paper, we introduce the representation theory of $\delta$-Hom-Jordan Lie conformal superalgebras and discuss the cases of adjoint representations. Furthermore, we develop the cohomology theory of Hom-Lie conformal superalgebras and…
In this paper, we show that the class of representable residuated semigroups has the finite representation property. That is, every finite representable residuated semigroup is isomorphic to some algebra over a finite base. This result…
The article is devoted to some ``strange'' phenomena of representation theory and their interrelations. Cross-projective representations of pairs of anticommutative algebras, alloys, their universal envelopping Lie algebras and their…
In this paper we study representations of ultragraph Leavitt path algebras via branching systems and, using partial skew ring theory, prove the reduction theorem for these algebras. We apply the reduction theorem to show that ultragraph…
We prove a theorem about the derivation algebra of the tensor product of two algebras. As an application, we determine the derivation algebra of the fixed point algebra of the tensor product of two algebras, with respect to the tensor…
This is a survey paper about affine Hecke algebras. We start from scratch and discuss some algebraic aspects of their representation theory, referring to the literature for proofs. We aim in particular at the classification of irreducible…