Related papers: On modules of linear transformations

We give a method of producing a Polish module over an arbitrary subring of $\mathbb Q$ from an ideal of subsets of $\mathbb N$ and a sequence in $\mathbb N$. The method allows us to construct two Polish $\mathbb Q$-vector spaces, $U$ and…

Linear relations, defined as submodules of the direct sum of two modules, can be viewed as objects that carry dynamical information and reflect the inherent uncertainty of sampled dynamics. These objects also provide an algebraic structure…

Let $G=(V,E)$ be a finite undirected graph. If $P$ is an oriented path from $r_1\in V$ to $r_2\in V$, we define $\partial(P) = r_2-r_1$. If $R, S\subseteq V$, we denote by $P(G; R, S)$ the span of the set of all $\partial P\otimes \partial…

Factoring out the spin $1$ subalgebra of a $ W $ algebra leads to a new $ W $ structure which can be seen either as a rational finitely generated $ W $ algebra or as a polynomial non-linear $ W_\infty$ realization.

Let $\Lambda$ be a commutative local uniserial ring of length at least seven with radical factor ring $k$. We consider the category $S(\Lambda)$ of all possible embeddings of submodules of finitely generated $\Lambda$-modules and show that…

Given a finite-dimensional complex Lie algebra g equipped with a nondegenerate, symmetric, invariant bilinear form B, let V_k(g,B) denote the universal affine vertex algebra associated to g and B at level k. For any reductive group G of…

Let g be a Lie bialgebra and let V be a finite-dimensional g-module. We study deformations of the symmetric algebra of V which are equivariant with respect to an action of the quantized enveloping algebra of g. In particular we investigate…

Let R be a commutative ring with identity and M be an R-module. The purpose of this paper is to introduced the dual notion of z-submodules of M and some of extensions. Moreover, we investigate some properties of these classes of modules…

All finite-dimensional Leibniz algebra bimodules of a Lie algebra $\mathfrak{sl}_2$ over a field of characteristic zero are described.

Let $p$ be a prime number, and $G$ a compact $p$-adic Lie group. We recall that the Iwasawa algebra $\Lambda(G)$ is defined to be the completed group ring of $G$ over the ring of $p$-adic integers. Interesting examples of finitely generated…

We study Translation functors and Wall-Crossing functors on infinite dimensional representations of a complex semisimple Lie algebra using D-modules. This functorial machinery is then used to prove the Endomorphism-theorem and the…

In this paper, we study contragredient duals and invariant bilinear forms for modular vertex algebras (in characteristic $p$). We first introduce a bialgebra $\mathcal{H}$ and we then introduce a notion of $\mathcal{H}$-module vertex…

An effective method to compute a presentation of $Tor_k (M,N)$ for modules on a not necessarily commutative algebra is proposed, more precisely when $R$ is a PBW algebra, $M$ is a centralizing $R$-bimodule and $N$ is a finitely generated…

If R is a commutative ring, we prove that every finitely generated module has a pure-composition series with indecomposable factors and any two such series are isomorphic if and only if R is a Bezout ring and a CF-ring.

Given a finite dimensional algebra $\Lambda$, we show that a frequently satisfied finiteness condition for the category ${\cal P}^{\infty}(\Lambda\rm{-mod})$ of all finitely generated (left) $\Lambda$-modules of finite projective dimension,…

Zassenhaus has proved that if U is a subnormal subalgebra of a finite-dimensional Lie algebra L and V is a finite-dimensional irreducible L-module, then all U-module composition factors of V are isomorphic. Schenkman has proved that if U is…

We classify all groups G and all pairs (V,W) of absolutely simple Yetter-Drinfeld modules over G such that the support of the direct sum of V and W generates G, the square of the braiding between V and W is not the identity, and the Nichols…

Let $V$ be a finite dimensional complex vector space and $W\subset \GL(V)$ be a finite complex reflection group. Let $V^{\reg}$ be the complement in $V$ of the reflecting hyperplanes. A classical conjecture predicts that $V^{\reg}$ is a…

The Hermitian, complex and fermionic two-matrix models with infinite set of variables are constructed. We show that these two-matrix models can be realized by the $W$-representations. In terms of the $W$-representations, we derive the…

This is a sequel to \cite{li-qva1} and \cite{li-qva2} in a series to study vertex algebra-like structures arising from various algebras such as quantum affine algebras and Yangians. In this paper, we study two versions of the double Yangian…