Noetherianity of the Space of Irreducible Representations

Irreducible and permutative representations of ultragraph Leavitt path algebras

We completely characterize perfect, permutative, irreducible representations of an ultragraph Leavitt path algebra. For this we extend to ultragraph Leavitt path algebras Chen's construction of irreducible representations of Leavitt path algebras. We show that these representations can be built from branching system and characterize irreducible representations associated to perfect branching systems. Along the way we improve the characterization of faithfulness of Chen's irreducible representations.

Irreducible representations of q-Schur superalgebras at a root of unity

Under the assumption that the quantum parameter $q$ is an $l$-th primitive root of unity with $l$ odd in a field $F$ of characteristic 0 and $m+n\geq r$, we obtained a complete classification of irreducible modules of the $q$-Schur superalgebra introduced H. Rui and the first Author.

Irreducible representations of the exceptional cheng-kac superalgebra

We classify all conformal irreducible modules of finite type over the Cheng Kac superalgebra CK(6).

Counting equivalence classes of irreducible representations

Let $n$ be a positive integer, and let $R$ be a (possibly infinite dimensional) finitely presented algebra over a computable field of characteristic zero. We describe an algorithm for deciding (in principle) whether $R$ has at most finitely many equivalence classes of $n$-dimensional irreducible representations. When $R$ does have only finitely many such equivalence classes, they can be effectively counted (assuming that $k[x]$ posesses a factoring algorithm).

Irreducible $SL_{n+1}$--Representations remain Indecomposable restricted to some Abelian Subalgebras

In this paper we show that any irreducible finite dimensional representation of $SL_{n+1}$ remains indecomposable if restricted to n--dimensional abelian subalgebras spanned by simple root vectors.

The irreducible representations of 3-dimensional Sklyanin algebras

In this article a complete description is given of the simple representations of a 3-dimensional Sklyanin algebra associated to a torsion point. In order to determine these irreducible representations, a review is given of classical results regarding representation theory of graded rings with excellent homological and algebraic properties.

Irreducible representations of Leavitt path algebras

We construct some irreducible representations of the Leavitt path algebra of an arbitrary quiver. The constructed representations are associated to certain algebraic branching systems. For a row-finite quiver, we classify algebraic branching systems, to which irreducible representations of the Leavitt path algebra are associated. For a certain quiver, we obtain a faithful completely reducible representation of the Leavitt path algebra. The twisted representations of the constructed ones under the scaling action are studied.

Bound for the cocharacters of the identities of irreducible representations of $\mathfrak{sl}_2(\mathbb{C})$

For each irreducible finite dimensional representation of the Lie algebra $\mathfrak{sl}_2(\mathbb{C})$ of $2\times 2$ traceless matrices, an explicit uniform upper bound is given for the multiplicities in the cocharacter sequence of the polynomial identities satisfied by the given representation.

Hom型扭Heisenberg-Virasoro代数的不可约表示

Irreducible representations of the twisted Heisenberg-Virasoro algebra of Hom type

本文针对Hom-李代数推广背景，研究Hom型扭Heisenberg-Virasoro代数的不可约表示，提出可由其诱导李代数的不可约表示诱导得到的方法，并构造了若干类该代数的不可约表示。

On the irreducible representation algebra of the alternating group of degree four

We obtain a description of the irreducible representation algebra of the alternating group of degree four over the ring of 2-adic integers.

Irreducible representations of the quantum Weyl algebra at roots of unity given by matrices

To describe the representation theory of the quantum Weyl algebra at an $l$th primitive root $γ$ of unity, Boyette, Leyk, Plunkett, Sipe, and Talley found all nonsingular irreducible matrix solutions to the equation $yx-γxy=1$, assuming $yx\neq xy$. In this note, we complete their result by finding and classifying, up to equivalence, all irreducible matrix solutions $(X, Y)$, where $X$ is singular.

On the Primitive Irreducible Representations of Finitely Generated Linear Groups of Finite Rank

In the paper we study finitely generated linear groups of finite rank which have faithful irreducible primitive representations over a field of characteristic zero. We prove that if an infinite finitely generated linear group $G$ of finite rank has a faithful irreducible primitive representation over a field of characteristic zero then the $FC$-center $Δ(G)$ of $G$ is infinite.

Irreducible representations of the Chinese monoid

All irreducible representations of the Chinese monoid $C_n$, of any rank $n$, over a nondenumerable algebraically closed field $K$, are constructed. It turns out that they have a remarkably simple form and they can be built inductively from irreducible representations of the monoid $C_2$. The proof shows also that every such representation is monomial. Since $C_n$ embeds into the algebra $K[C_n]/J(K[C_n])$, where $J(K[C_n])$ denotes the Jacobson radical of the mooned algebra $K[C_n]$, a new representation of $C_n$ as a subdirect product of the images of $C_n$ in the endomorphism algebras of th…

Periodic subvarieties of semiabelian varieties and annihilators of irreducible representations

Let $G$ be a semiabelian variety defined over a field of characteristic $0$, endowed with an endomorphism $Φ$. We prove there is no proper subvariety $Y\subset G$ which intersects the orbit of each periodic point of $G$ under the action of $Φ$. As an application, we are able to give a topological characterization of the annihilator ideals of irreducible representations in certain skew polynomial algebras.

Most irreducible representations of the 3-string braid group

As the 3-string braid group B(3) and the modular group PSL(2,Z) are both of wild representation type one cannot expect a full classification of all their finite dimensional simple representations. Still, one can aim to describe 'most' irreducible representations by constructing for each d-dimensional irreducible component X of the variety iss(n,B(3)) classifying the isomorphism classes of semi-simple n-dimensional representations of B(3) an explicit minimal etale rational map A^d --> X having a Zariski dense image. Such rational dense parametrizations were obtained for all components when n < …

单边子位移代数的不可约表示

Irreducible representations of one-sided subshift algebras

本文构造了任意字母表上子位移相关有单位代数的表示，用无出口循环描述其忠实性准则，刻画不可约分量等价性，并确定与线路径相关的极小左理想。