相关论文: $A^{N}_{\infty}$-algebras

We show that the method to construct C^*-algebras from topological graphs, introduced in our previous paper, generalizes many known constructions. We give many ways to make new topological graphs from old ones, and study the relation of…

This is a survey on the finite basis problem for varieties of algebraic systems. Our exposition is in two directions: (i) We give numerous examples of varieties which are not finitely based. (ii) We give examples of important varieties with…

In this paper, we focus on $(n+3)$-dimensional metric $n$-Lie algebras. To begin with, we give some properties on $(n+3)$-dimensional $n$-Lie algebras. Then based on the properties, we obtain the classification of $(n+3)$-dimensional metric…

The integrability condition called shape invariance is shown to have an underlying algebraic structure and the associated Lie algebras are identified. These shape-invariance algebras transform the parameters of the potentials such as…

We prove explit formulas for the decomposition of a differential graded Lie algebra into a minimal and a linear $L_\infty$-algebra. We define a category of metric $L_\infty$-algebras, called Palamodov $L_\infty$ algebras, where the…

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 variety of Leibniz algebras. It is shown that, up to isomorphism, there exist three…

Classification, up to isomorphism, of algebras from a non-empty subset of the variety of $n$- dimensional algebras is presented. It is shown that these algebras have only trivial automorphism and if the basic field is algebraically closed…

In this article we define $G$-algebras, that is, graded algebras on which a reductive group $G$ acts as gradation preserving automorphisms. Starting from a finite dimensional $G$-module $V$ and the polynomial ring $\mathbb{C}[V]$, it is…

We develop axiomatics of highest weight categories and quasi-hereditary algebras in order to incorporate two semi-infinite situations which are in Ringel duality with each other; the underlying posets are either upper finite or lower…

A new class of infinite dimensional simple Lie algebras over a field with characteristic 0 are constructed. These are examples of non-graded Lie algebras. The isomorphism classes of these Lie algebras are determined. The structure space of…

Covering Algebras of extended affine Lie algebras(EALA's) relative to finite order automorphisms are studied. Conditions are given for when the resulting algebra is again an EALA. This paper deals with affinizations of EALA's relative to…

In this work $n$-dimensional filiform Leibniz algebras admitting a gradation of length $(n-1)$ are classified. Derivations of such algebras are also described.

This paper is devoted to the study of multigraded algebras and multigraded linear series. For an $\mathbb{N}^s$-graded algebra $A$, we define and study its volume function $F_A:\mathbb{N}_+^s\to \mathbb{R}$, which computes the asymptotics…

We begin the systematic model theoretic study of $\mathrm{C}^*$-algebras using the tools of continuous logic.

In this article we prove various results about transferring or lifting $\mathrm{A}_\infty$-algebra structures along quasi-isomorphisms over a commutative ring.

This work adapts the equivalent definitions of division algebras over a field into multiple types of division algebras in a monoidal category. Examples and consequences of these definitions are then established in various monoidal settings.

Triangular algebras, and maximal triangular algebras in particular, have been objects of interest for over fifty years. Rich families of examples have been studied in the context of many w$^*$- and C$^*$-algebras, but there remains a dearth…

We study complex projective varieties that parametrize (finite-dimensional) filiform Lie algebras over C, using equations derived by Millionshchikov. In the infinite-dimensional case we concentrate our attention on N-graded Lie algebras of…

Leibniz algebras ${\mathcal E}_n$ were introduced as algebraic structure underlying U-duality. Algebras ${\mathcal E}_3$ derived from Bianchi three-dimensional Lie algebras are classified here. Two types of algebras are obtained:…

Curved A-infinity algebras appear in nature as deformations of dg algebras. We develop the basic theory of curved A-infinity algebras and, in particular, curved dg algebras. We investigate their link with a suitable class of dg coalgebras…