相关论文: Structures and Representations of Generalized Path…

A classical theorem of R. Baer describes the nilpotent radical of a finite group G as the set of all Engel elements, i.e. elements y in G such that for any x in G the n-th commutator [x,y,...,y] equals 1 for n big enough. We obtain a…

Let $\Lambda$ be a finite dimensional algebra and $G$ be a finite group whose elements act on $\Lambda$ as algebra automorphisms. Under the assumption that $\Lambda$ has a complete set $E$ of primitive orthogonal idempotents, closed under…

An approach to representations of finite groups is presented without recourse to character theory. Considering the group algebra C[G] as an algebra of linear maps on C[G] (by left multiplication), we derive the primitive central idempotents…

In this paper we study the graded version of Naimark's problem for Leavitt path algebras considering them as $\mathbb{Z}$-graded algebras. Several characterizations are obtained of a Leavitt path algebra $L$ of an arbitrary graph $E$ over a…

Let $Q$ be a Dynkin quiver and $\Pi$ the corresponding set of positive roots. For the preprojective algebra $\Lambda$ associated to $Q$ we produce a rigid $\Lambda$-module $I_Q$ with $r=|\Pi|$ pairwise non-isomorphic indecomposable direct…

If a geometry $\Gamma$ is isomorphic to the residue of a point $A$ of a shadow geometry of a spherical building $\Delta$, a representation $\varepsilon_\Delta^A$ of $\Gamma$ can be given in the unipotent radical $U_{A^*}$ of the stabilizer…

In this article we prove that there exists a Dixmier map for nilpotent super Lie algebras. In other words, if we denote by Prim(U(g)) the set of (graded) primitive ideals of the enveloping algebra U(g) of g and Ad_0 the adjoint group of…

We generalize earlier results about connected components of idempotents in Banach algebras, due to B. Sz\H{o}kefalvi Nagy, Y. Kato, S. Maeda, Z. V. Kovarik, J. Zem\'anek, J. Esterle. Let $A$ be a unital complex Banach algebra, and…

Let $R=\oplus_{\Gamma\in\Gamma}R_{\gamma}$ be a $\Gamma$-graded $K$-algebra over a field $K$, where $\Gamma$ is a totally ordered semigroup, and let $I$ be an ideal of $R$. Considering the $\Gamma$-grading filtration $FR$ of $R$ and the…

In this paper, we describe primitive ideal space of the $C^*$-algebra $C^*(\Lambda)$ associated to any locally convex row-finite $k$-graph $\Lambda$. To do this, we will apply the Farthing's desourcifying method on a recent result of…

Let $\Lambda = \mathbb{Z}^n$ with lexicographic ordering. $\Lambda$ is a totally ordered group. Let $X = \Lambda^+ * \Lambda^+$. Then $X$ is a $\Lambda$-tree. Analogous to the construction of graph $C^*$-algebras, we form a groupoid whose…

We present a simple combinatorial model for the characters of the irreducible integrable highest weight modules for complex symmetrizable Kac-Moody algebras. This model can be viewed as a discrete counterpart to the Littelmann path model.…

By combining well-known techniques from both noncommutative algebra and computational commutative algebra, we observe that an algorithmic approach can be applied to the study of irreducible representations of finitely presented algebras. In…

Let $k$ be an arbitrary field, $\Lambda$ be a $k$-algebra and $V$ be a $\Lambda$-module. When it exists, the universal deformation ring $R(\Lambda,V)$ of $V$ is a $k$-algebra whose local homomorphisms to $R$ parametrize the lifts of $V$ up…

In this paper we completely describe graphically Leavitt path algebras with bounded index of nilpotence and show that each graded simple module $S$ over a Leavitt path algebra with bounded index of nilpotence is graded $\Sigma$-injective,…

For a set $\Gamma$, a function $\lambda:\Gamma\to \Gamma$ and a non-trivial abelian group $K$, the generalized shift $\sigma_\lambda:K^\Gamma\to K^\Gamma$ is defined by $(x_i)_{i\in \Gamma}\mapsto (x_{\lambda(i)})_{i\in\Gamma}$. In this…

In this monograph we undertake a comprehensive study of separable representations (as well as their unitary equivalence classes) of $C^*$-algebras associated to strongly connected finite $k$-graphs $\Lambda$. We begin with the…

Given a finitely aligned $k$-graph $\Lambda$, we let $\Lambda^i$ denote the $(k-1)$-graph formed by removing all edges of degree $e_i$ from $\Lambda$. We show that the Toeplitz-Cuntz-Krieger algebra of $\Lambda$, denoted by…

Using the syzygy method, established in our earlier paper, we characterize the combinatorial stratification of the variety of two-dimensional real generic algebras. We show that there exist exactly three different homotopic types of such…

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 $a_{1}a_{2}... a_{n} =a_{\sigma (1)} a_{\sigma (2)} ... a_{\sigma (n)}$, where $\sigma$…