Related papers: Finite Implication Algebras
Quantum implication algebras without complementation are formulated with the same axioms for all five quantum implications. Previous formulations of orthoimplication, orthomodular implication, and quasi-implication algebras are analysed and…
Boolean-type algebra (BTA) is investigated. A BTA is decomposed into Boolean-type lattice (BTL) and a complementation algebra (CA). When the object set is finite, the matrix expressions of BTL and CA (and then BTA) are presented. The…
We introduce the notion of ends for algebras. The definition is analogous to the one in geometric group theory. We establish some relations to growth conditions and cyclic cohomology.
We describe isomorphisms of groups of several periodic infinite matrices and isomorphisms of groups of invertible elements of unital locally matrix algebras.
We consider the functions in two variables on an arbitrary poset, for which the convolution operation is defined. We obtain the generalization of incidence algebra and describe its properties: invertibility, the Jackobson radical,…
Primarily this paper presents an expository report on alternatives to the traditional methods of classifying representations of finite dimensional algebras. Some new results illustrating such alternatives for algebras with only finitely…
We discuss the noncommutative generalizations of polynomial algebras which after appropriate completions can be used as coordinate algebras in various noncommutative settings, (noncommutative differential geometry, noncommutative algebraic…
We present a necessary and sufficient condition for a Boolean algebra to carry a finitely additive measure.
We classify mutation-finite cluster algebras with arbitrary coefficients of geometric type.
A finite W-algebra is an associative algebra constructed from a semisimple Lie algebra and its nilpotent element. In this survey we review recent developments in the representation theory of W-algebras. We emphasize various interactions…
Several structural properties of a universal algebra can be seen from the higher commutators of its congruences. Even on a finite algebra, the sequence of higher commutator operations is an infinite object. In the present paper, we exhibit…
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 the last years a lot of work has been concentrated on the study of the behaviour at infinity of polynomial maps. This behaviour can be very complicated, therefore the main idea was to find special classes of polynomial maps which have,…
We give criteria for finite dimensionality or infinite dimensionality of the polynomial centralizer of the Lie algebra of a linear Lie group, in terms of invariants and relative invariants of the group. In the finite dimensional scenario…
We establish several finiteness properties of groups defined by algebraic difference equations. One of our main results is that a subgroup of the general linear group defined by possibly infinitely many algebraic difference equations in the…
A characterization of the maximal abelian sub-algebras of matrix algebras that are normalized by the canonical representation of a finite Heisenberg group is given. Examples are constructed using a classification result for finite…
A correspondence between a monogenic function in an arbitrary finite-dimensional commutative associative algebra and a finite set of monogenic functions in a special commutative associative algebra is established.
To each associative unitary finite-dimensional algebra over a normal base, we associative a canonical multiplicative function called its determinant. We give various properties of this construction, as well as applications to the topology…
In this paper, we present a general framework for the derivation of interesting finite combinatorial sums starting with certain classes of polynomial identities. The sums that can be derived involve products of binomial coefficients and…
We derive "numerical" criteria for the existence of embeddings of representations of finite dimensional algebras.