相关论文: Notes on normed algebras
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
Symmetries for wave equation with additional conditions are found. Some conditions yield infinite-dimensional symmetry algebra for the nonlinear equation. Ansatzes and solutions corresponding to the new symmetries were constructed.
We introduce order conserving embeddings as a more general form of order preserving embeddings between finite dimensional nest algebras. The structure of these embeddings is determined, in terms of order indecomposable decompositions, and…
The work is devoted to the variety of $2$-dimensional algebras over an algebraically closed field. Firstly, we classify such algebras modulo isomorphism. Then we describe the degenerations and the closures of principal algebra series in the…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.
We suggest a few projects for studying vertex algebras with emphasis on finite group viewpoints.
Let $A$ be an Artin algebra. We investigate subalgebras of $A$ with certain conditions and obtain some classes of algebras whose finitistic dimensions are finite.
These lecture notes for the 2013 CIME/CIRM summer school Combinatorial Algebraic Geometry deal with manifestly infinite-dimensional algebraic varieties with large symmetry groups. So large, in fact, that subvarieties stable under those…
This paper is devoted to the description of complex finite-dimensional algebras of level two. We obtain the classification of algebras of level two in the varieties of Jordan, Lie and associative algebras.
The input and output algebras of an infinite qubit system and their representations are described.
This book treats: - spectral theory of Banach *-algebras, - basic representation theory of normed *-algebras, - spectral theory of representations of commutative *-algebras. A novel feature of the book is the construction of the enveloping…
We discuss some basic properties of the graded center of a triangulated category and compute examples arising in representation theory of finite dimensional algebras.
The purpose of this paper is to investigate finite-dimensional superbialgebras and Hopf superalgebras. We study connected superbialgebras and provide a classification of non-trivial superbialgebras and Hopf superalgebras in dimension $n$…
Affiliated and normal operators in octonion Hilbert spaces are studied. Theorems about their properties and of related algebras are demonstrated. Spectra of unbounded normal operators are investigated.
These notes concern linear transformations on R^n and C^n, exponentials of linear transformations, and some related geometric questions.
This is a detailed survey -- with rigorous and self-contained proofs -- of some of the basics of elementary combinatorics and algebra, including the properties of finite sums, binomial coefficients, permutations and determinants. It is…
A little general abstract combinatorial nonsense delivered in this note is a presentation of some old and basic concepts, central to discrete mathematics, in terms of new words. The treatment is from a structural and systematic point of…
The present paper is devoted to the description of finite-dimensional semisimple Leibniz algebras over complex numbers, their derivations and automorphisms.
We investigate the spectrum and the essential spectra of weighted automorphisms of the polydisc algebra $\mathbb{A}^n$. In the case $n=2$ we provide a detailed and, in most cases, complete description of these spectra.
Two examples of spectral triples with non-integer dimension spectrum are considered. These triples involve commutative C*-algebras. The first example has complex dimension spectrum and trivial differential algebra. The other is a parameter…