相关论文: Relational Algebra as non-Distributive Lattice

Axial algebras are a recently introduced class of non-associative algebra motivated by applications to groups and vertex-operator algebras. We develop the structure theory of axial algebras focussing on two major topics: (1) radical and…

We examine two nonselfadjoint operator algebras: the weighted shift algebra, and the Volterra operator algebra. In both cases, the operator algebra is the norm closure of the polynomials in the operator norm. In the case of the weighted…

Absolute algebras are a new type of algebraic structures, endowed with a meaningful notion of infinite sums of operations without supposing any underlying topology. Opposite to the usual definition of operadic calculus, they are defined as…

We study so called regular Lie algebras, i.e. Lie algebras in which each nonzero element is regular. We make a connection with an open problem whether any element of reduced trace zero in a simple associative algebra is a commutator.

We study actions of connected algebraic groups on normal algebraic varieties, and show how to reduce them to actions of affine subgroups.

The classical propositional logic is known to be sound and complete with respect to the set semantics that interprets connectives as set operations. The paper extends propositional language by a new binary modality that corresponds to…

We present some general theorems about operator algebras that are algebras of functions on sets, including theories of local algebras, residually finite dimensional operator algebras and algebras that can be represented as the scalar…

The main non-associative algebras are Lie algebras and Jordan algebras. There are several ways to unify these non-associative algebras and associative algebras.

These are lecture notes on the algebraic approach to regular languages. The classical algebraic approach is for finite words; it uses semigroups instead of automata. However, the algebraic approach can be extended to structures beyond…

The notion of associativity (which differs from the straightforward generalization of the usual associativity given by the move of parentheses in the relevant expression) for operations of high arity is introduced. It is proved that the…

In this paper it is shown that the lattice of C*-covers of an operator algebra does not contain enough information to distinguish operator algebras up to completely isometric isomorphism. In addition, four natural equivalences of the…

We give an algebraic proof of the unitarity of the vertex operator algebra $L(21/22, 0)\oplus L(21/22, 8)$ and of all its irreducible ordinary modules, using a coset realization arising from the $3C$-algebra. Motivated by the structure of…

We generalize the solution of linear recurrence relations from fields to central division algebras, adapting the standard tools of companion matrices and characteristic polynomials to the non-commutative setting. We then solve linear…

In relational approach to general rough sets, ideas of directed relations are supplemented with additional conditions for multiple algebraic approaches in this research paper. The relations are also specialized to representations of general…

We argue that operads provide a general framework for dealing with polynomials and combinatory completeness of combinatory algebras, including the classical $\mathbf{SK}$-algebras, linear $\mathbf{BCI}$-algebras, planar…

Bases, mappings, projections and metrics, natural for Neural network training, are introduced. Graph-theoretical interpretation is offered. Non-Gaussianity naturally emerges, even in relatively simple datasets. Training statistics,…

Although algebraic structures are frequently analyzed using unary and binary operations, they can also be effectively defined and unified through ternary operations. In this context, we introduce structures that contain two constants and a…

Over a field of characteristic zero we prove two formality conditions. We prove that a dg Lie algebra is formal if and only if its universal enveloping algebra is formal. We also prove that a commutative dg algebra is formal as a dg…

A function on an algebra is congruence preserving if, for any congruence, it maps pairs of congruent elements onto pairs of congruent elements. We show that on the algebra of complete binary trees whose leaves are labeled by letters of an…

The Leibniz bracket of an operator on a (graded) algebra is defined and some of its properties are studied. A basic theorem relating the Leibniz bracket of the commutator of two operators to the Leibniz bracket of them, is obtained. Under…