相关论文: Notes on normed algebras
These notes give an elementary approach to parts of the theory of standard Borel and analytic spaces.
In this survey we discuss the results on the finitistic dimension of various stratified algebras. We describe what is already known, present some recent estimates, and list some open problems.
We define graded Hopf algebras with bases labeled by various types of graphs and hypergraphs, provided with natural embeddings into an algebra of polynomials in infinitely many variables. These algebras are graded by the number of edges and…
In this essay, we immerse into the framework of normed division algebras as a suitable arena to accommodate the standard model of elementary particles, and we explore some applications to cosmology. Remarkably, they permit interesting…
We give a summary on spectral techniques for finite dimensional algebras and study its link to singularity theory. In particular, we offer a contribution to the categorification of the Milnor lattice of two-dimensional singularities through…
In this note one tries to venture into a study of some notions, in the context of a (unital) normed algebra, in particular the algebra of operators on a Hilbert space. Namely, one considers ``moving norms'', i.e.\ norming an element minus a…
Similar to linear spaces, many examples of quasilinear spaces have a notion of multiplication of the elements. To characterising these examples, in the present paper we generalize the notion of quasilinear spaces and introduce…
These are expanded notes of four introductory talks on A-infinity algebras, their modules and their derived categories.
In this paper we introduce a new property for normed algebras. This property which we call it stability, plays a key role in the studying of the theory of almost multiplier maps. In this note we study some of the basic properties of this…
Let $\Lambda$ be a finite dimensional algebra over an algebraically closed field $k$. We survey some results on algebras of finite global dimension and address some open problems.
This is a survey on the state-of-the-art of the classification of finite-dimensional complex Hopf algebras. This general question is addressed through the consideration of different classes of such Hopf algebras. Pointed Hopf algebras…
In this paper, we describe an elementary method for counting the number of non-isomorphic algebras of a fixed dimension over a given finite field. We show how this method works for the explicit example of $2$-dimensional algebras over the…
These informal notes deal with a number of questions related to sums and integrals in analysis.
We define the probability of an equation in a finite algebra as the proportion of tuples in its domain that satisfy it. We call the probabilistic spectrum of an algebra the set of probability values obtained when the equation varies. We…
We obtain a description of the spectrum of bidual algebra $A^{**}$ of a uniform algebra $A$. This spectrum turns out to be a quotient space of the hyper-Stonean envelope of the spectrum of $A$.
We characterize vertex algebras (in a suitable sense) as algebras over a certain graded co-operad. We also discuss some examples and categorical implications of this characterization.
These notes include introductory material on the notion of splitting fields for modules over a k-algebra where k is a field.
To a regular projection of a knot we associate a finite dimensional non-commutative associative algebra which is self-injective and special biserial.
There are versions of "calculus" in many settings, with various mixtures of algebra and analysis. In these informal notes we consider a few examples that suggest a lot of interesting questions.
In the present paper we obtain the list of algebras, up to isomorphism, such that closure of any complex finite-dimensional algebra contains one of the algebra of the given list.