Related papers: Infinite-Dimensional Triangularizable Algebras

We prolonge the list of C*-algebras for which all extensions by any stable separable C*-algebra are semi-invertible. In particular, we handle certain amalgamations, both of C*-algebras and of groups. Concerning groups we consider both…

Let $T(X)$ (resp. L(V)) be the semigroup of all transformations (resp. linear transformations) of a set $X$ (resp. vector space $V$). For a subset $Y$ of $X$ and a subsemigroup $\mathbb{S}(Y)$ of $T(Y)$, consider the subsemigroup…

Over fields of arbitrary characteristic we classify all rank three Nichols algebras of diagonal type with a finite root system. Our proof uses the classification of the finite Weyl groupoids of rank three.

We define the spectrum of a tensor triangulated category $K$ as the set of so-called prime ideals, endowed with a suitable topology. In this very generality, the spectrum is the universal space in which one can define supports for objects…

Let $V$ be a simple vertex operator superalgebra and $G$ a finite automorphism group of $V$ containing the canonical automorphism $\sigma$ such that $V^G$ is regular. It is proved that every irreducible $V^G$-module occurs in an irreducible…

A finite graph is called a tricirculant if admits a cyclic group of automorphism which has precisely three orbits on the vertex-set of the graph, all of equal size. We classify all finite connected cubic vertex-transitive tricirculants. We…

In many instances in first order logic or computable algebra, classical theorems show that many problems are undecidable for general structures, but become decidable if some rigidity is imposed on the structure. For example, the set of…

A systematic method is presented for the construction and classification of algebras of gauge transformations for arbitrary high rank tensor gauge fields. For every tensor gauge field of a given rank, the gauge transformation will be…

We show that if $V$ is a vertex operator algebra such that all the irreducible ordinary $V$-modules are $C_1$-cofinite and all the grading-restricted generalized Verma modules for $V$ are of finite length, then the category of finite length…

Over fields of characteristic zero, we determine all absolutely irreducible Yetter-Drinfeld modules over groups that have prime dimension and yield a finite-dimensional Nichols algebra. To achieve our goal, we introduce orders of braided…

We define the Hall algebra associated to any triangulated category under some finiteness conditions with the $t$-periodic translation functor $T$ for odd $t>1.$ This generalizes the results in \cite{Toen2005} and \cite{XX2006}.

We prove that if A is a finite algebra with a parallelogram term that satisfies the split centralizer condition, then A is dualizable. This yields yet another proof of the dualizability of any finite algebra with a near unanimity term, but…

An infinite filiform Lie algebra L is residually nilpotent and its graded associated with respect to the lower central series has smallest possible dimension in each degree but is still infinite. This means that gr(L) is of dimension two in…

A finite-dimensional Lie algebra is called an A-algebra if all of its nilpotent subalgebras are abelian. These arise in the study of constant Yang-Mills potentials and have also been particularly important in relation to the problem of…

This paper gives an analogue of A_g(V) theory for a vertex operator superalgebra V and an automorphism g of finite order. The relation between the g-twisted V-modules and A_g(V)-modules is established. It is proved that if V is g-rational,…

Let L be a Lie pseudoalgebra, a in L. We show that, if a generates a (finite) solvable subalgebra S=<a>, then one may find a lifting a' in S of [a] in S/S' such that <a'> is nilpotent. We then apply this result towards vertex algebras: we…

A triangular limit algebra A is isometrically isomorphic to the tensor algebra of a C*-correspondence if and only if its fundamental relation R(A) is a tree admitting a $Z^+_0$-valued continuous and coherent cocycle. For triangular limit…

Let $K$ be a field, $\mathcal {O}_v$ a valuation ring of $K$ associated to a valuation $v$: $K\rightarrow\Gamma\cup\{\infty\}$, and ${\bf m}_v$ the unique maximal ideal of $\mathcal {O}_v$. Consider an ideal $\mathcal {I}$ of the free…

A linear mapping upon real n-dimensional space, where the dimension n is odd, has a real eigenvalue-eigenvector pair. The corresponding statement for complex vector spaces holds true for any dimension n, but should be easy to demonstrate…

We achieve an extremely useful description (up to isomorphism) of the Leavitt path algebra $L_K(E)$ of a finite graph $E$ with coefficients in a field $K$ as a direct sum of matrix rings over $K$, direct sum with a corner of the Leavitt…