Related papers: A Finite Dimensional $A_{\infty}$ Algebra Example
In this article we construct a new class of finite dimensional irreducible modules genaralizing evaluation modules for multiloop superalgebra of type A(m,n) and C(m). We prove that these are the only such modules. In all other cases it is…
We describe the structure of finite dimensional selfinjective algebras over an arbitrary field without short cycles of indecomposable modules.
In this paper we characterize finite effect algebras which have a state. We construct two matrices $A$ and $B$ assigned to a finite effect algebra $E$ and show that if $E$ has a state then rank$A=$ rank$B$.
In an earlier paper, we described bordered algebras for knot Floer homology. In this paper, we introduce a differential graded algebra, the pong algebra and compute the A-infinity structure on its homology.
In this note, we investigate how different fundamental groups of presentations of a fixed algebra $A$ can be. For finitely many finitely presented groups $G_i$, we construct an algebra $A$ such that all $G_i$ appear as fundamental groups of…
The objective of this paper is to determine the finite dimensional, indecomposable representations of the algebra that is generated by two complex structures over the real numbers. Since the generators satisfy relations that are similar to…
In this paper, we establish two finiteness results and propose a conjecture concerning the Pythagoras number $P(A)$ of a finitely generated real algebra $A$. Let $X \hookrightarrow \mathbb{P}^n$ be an integral projective surface over…
We look at spaces of infinite-by-infinite matrices, and consider closed subsets that are stable under simultaneous row and column operations. We prove that up to symmetry, any of these closed subsets is defined by finitely many equations.
In this paper we determine the representation type of some algebras of infinite matrices continuously controlled at infinity by a compact metrizable space. We explicitly classify their finitely presented modules in the finite and tame…
We classify $n$-representation infinite algebras $\Lambda$ of type \~A. This type is defined by requiring that $\Lambda$ has higher preprojective algebra $\Pi_{n+1}(\Lambda) \simeq k[x_1, \ldots, x_{n+1}] \ast G$, where $G \leq…
We compute the graded polynomial identities of the infinite dimensional upper triangular matrix algebra over an arbitrary field. If the grading group is finite, we prove that the set of graded polynomial identities admits a finite basis. We…
Enveloping $C^*$-algebras for some finitely generated $*$-algebras are considered. It is shown that all of the considered algebras are identically defined by their dual spaces. The description in terms of matrix-functions is given. Keywords…
We construct an algebra of dimension $2^{\aleph_0}$ consisting only of functions which in no point possess a finite one-sided derivative. We further show that some well known nowhere differentiable functions generate algebras, which contain…
We prove that the genus of a finite-dimensional division algebra is finite whenever the center is a finitely generated field of any characteristic. We also discuss potential applications of our method to other problems, including the…
The well-behaved representations of the coordinate algebra of a 2-dimensional quantum complex plane are classified and a C*-algebra is defined which can be viewed as the algebra of continuous functions on the 2-dimensional quantum complex…
We present new examples of finite-dimensional Nichols algebras over fields of positive characteristic. The corresponding braided vector spaces are not of diagonal type, admit a realization as Yetter-Drinfeld modules over finite abelian…
In this work we construct a infinite dimensional $\ell$-super Galilean conformal algebra, which is a generalization of the $\ell=1$ algebra found in the literature. We give a classification of central extensions, the vector field…
In previous work we showed that the contact category algebra of a quadrangulated surface is isomorphic to the homology of a strand algebra from bordered sutured Floer theory. Being isomorphic to the homology of a differential graded…
We introduce the notion of a cellular system in order to deal with quasi-hereditary algebras. We shall prove that a necessary and sufficient condition for an algebra to be quasi-hereditary is the existence of a full divisible cellular…
The paper deals with a construction of a separating system of rational invariants for finite dimensional generic algebras. In the process of dealing an approach to a rough classification of finite dimensional algebras is offered by…