Related papers: Idempotent systems and character algebras
Matsuo algebras are an algebraic incarnation of 3-transposition groups with a parameter $\alpha$, where idempotents takes the role of the transpositions. We show that a large class of idempotents in Matsuo algebras satisfy the Seress…
Lie admissible algebra structures, called center-symmetric algebras, are defined. Main properties and algebraic consequences are derived and discussed. Bimodules are given and used to build a center-symmetric algebra on the direct sum of…
In this paper we introduce a new ingredient, invariant systems of differential equations, to our study of character sheaves on graded Lie algebras. The character sheaves we construct in this paper, together with the ones constructed in…
Via the transverse Hilbert scheme construction, we associate a holomorphic completely integrable system to a surface $S$ endowed with a holomorphic symplectic form $\omega$ and a projection onto $\mathbb{C}$. We provide a full…
It is well known that over an infinite field the ring of symmetric functions in a finite number of variables is isomorphic to the one of polynomial functions on matrices that are invariants by the action of conjugation by general linear…
In this paper we characterize the effect algebras whose sharp and principal elements coincide. We also give examples of two non-isomorphic effect algebras having the same universum, partial order and orthosupplementation.
In this paper we study structural properties of residuated lattices that are idempotent as monoids. We provide descriptions of the totally ordered members of this class and obtain counting theorems for the number of finite algebras in…
Nilpotent Leibniz algebras with isomorphic maximal subalgebras are considered. The algebras are classified for coclass zero, one, and two. The results are field dependent.
In the study of pre-Lie algebras, the concept of pre-morphism arises naturally as a generalization of the standard notion of morphism. Pre-morphisms can be defined for arbitrary (not-necessarily associative) algebras over any commutative…
We show that the question whether a term is typable is decidable for type systems combining inclusion polymorphism with parametric polymorphism provided the type constructors are at most unary. To prove this result we first reduce the…
The classical characteristic map associates symmetric functions to characters of the symmetric groups. There are two natural analogues of this map involving the Brauer algebra. The first of them relies on the action of the orthogonal or…
We assign a relational structure to any finite algebra in a canonical way, using solution sets of equations, and we prove that this relational structure is polymorphism-homogeneous if and only if the algebra itself is…
Let $V$ be a complete discrete valuation ring, and let $G$ be either a word-hyperbolic group or a reductive $p$-adic group. We prove that the canonical morphism $V[G] \to V[G]^\dagger$ from the group algebra to its dagger completion is an…
In these notes we develop some basic theory of idempotents in monoidal categories. We introduce and study the notion of a pair of complementary idempotents in a triangulated monoidal category, as well as more general idempotent…
Starting from involutive BE algebras, we redefine the orthomodular algebras, by introducing the notion of implicative-orthomodular algebras. We investigate properties of implicative-orthomodular algebras, and give characterizations of these…
In this paper we consider some classical varieties of linear algebras over the field which has characteristic 0. For every considered variety we take a category of the finite generated free algebras of this variety. And for every this…
In quantum mechanics, associative algebras play an important role in understanding symmetries and operator algebras, providing new algebraic frameworks for describing physical systems. This work classifies associative algebras over a field…
In the variety of all linear algebras over the infinite field the difference between geometric and automorphic equivalence of algebras can be big.
Motivated by the search for idempotent cellular automata (CA), we study CA that act almost as the identity unless they read a fixed pattern $p$. We show that constant and symmetrical patterns always produce idempotent CA, and we…
We give a survey of recent results related to the problem of characterizing finite-dimensional division algebras by the set of isomorphism classes of their maximal subfields. We also discuss various generalizations of this problem and some…