Related papers: Congruence FD-maximal varieties of algebras
We prove that for any finite-dimensional differential graded algebra with separable semisimple part the category of perfect modules is equivalent to a full subcategory of the category of perfect complexes on a smooth projective scheme with…
We give a complete description of the congruence lattices of the following finite diagram monoids: the partition monoid, the planar partition monoid, the Brauer monoid, the Jones monoid (also known as the Temperley-Lieb monoid), the Motzkin…
For an arbitrary finite dimensional algebra $\Lambda$, we prove that any wide subcategory of $\mathsf{mod} \Lambda$ satisfying a certain finiteness condition is $\theta$-semistable for some stability condition $\theta$. More generally, we…
In this paper we classify the isomorphism classes of four dimensional nilpotent associative algebras over a field F, studying regular subgroups of the affine group AGL_4(F). In particular we provide explicit representatives for such classes…
The purpose of this paper is to consider when two maximal subalgebras of a finite-dimensional solvable Lie algebra $L$ are conjugate, and to investigate their intersection.
Let $T_X$ be the full transformation monoid over a finite set $X$, and fix some $a\in T_X$ of rank $r$. The variant $T_X^a$ has underlying set $T_X$, and operation $f\star g=fag$. We study the congruences of the subsemigroup $P=Reg(T_X^a)$…
In this note we study the finite groups whose subgroup lattices are dismantlable.
We characterize the finite intervals of the Muchnik lattice by proving that they are a certain proper subclass of the finite distributive lattices.
Following ideas of Lawvere and Linton we prove that classical varieties are precisely the exact categories with a varietal generator. This means a strong generator which is abstractly finite and regularly projective. An analogous…
This paper studies absolute retracts in congruence modular varieties of universal algebras. It is shown that every absolute retract with finite dimensional congruence lattice is a product of subdirectly irreducible algebras. Further, every…
We investigate the structure of maximal commutative subalgebras of the finite dimensional Grassmann algebra over a field of characteristic different from two.
We give a full classification, up to equivalence, of finite-dimensional graded division algebras over the field of real numbers. The grading group is any abelian group.
We characterize when a finite lattice is distributive by the existences of some particular classes of Koszul filtrations.
We prove that the representations numbers of a ternary definite integral quadratic form defined over F_q[t], where F_q is a finite field of odd characteristic, determine its integral equivalence class when q is large enough with respect to…
Several results on presenting an affine algebraic group variety as a product of algebraic varieties are obtained.
Let A be a finitely generated associative algebra over an algebraically closed field. We characterize the finite dimensional modules over A whose orbit closures are regular varieties.
Meet semidistributive varieties are in a sense the last of the most important classes in universal algebra for which it is unknown whether it can be characterized by a strong Maltsev condition. We present a new, relatively simple Maltsev…
In this paper, a subclass of bounded distributive lattices, that is, finitely disjunctive distributive lattices (FDD-lattices) have been introduced. Then we apply it to establish a Stone duality for Lawson compact algebraic L-domains.…
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…
This paper presents a unified framework for determining the congruences on a number of monoids and categories of transformations, diagrams, matrices and braids, and on all their ideals. The key theoretical advances present an iterative…