Related papers: The Riesz hull of a semisimple MV-algebra
MV-monoids are algebras $\langle A,\vee,\wedge, \oplus,\odot, 0,1\rangle$ where $\langle A, \vee, \wedge, 0, 1\rangle$ is a bounded distributive lattice, both $\langle A, \oplus, 0 \rangle$ and $\langle A, \odot, 1\rangle$ are commutative…
We introduce the notions of multi-suprema and multi-infima for vector spaces equipped with a collection of wedges, generalizing the notions of suprema and infima in ordered vector spaces. Multi-lattices are vector spaces closed under…
A Lax operator algebra is constructed for an arbitrary semi-simple Lie algebra over $\mathbb C$ equipped with a $\mathbb Z$-grading, and arbitrary compact Riemann surface with marked points. In this set-up, a treatment of almost graded…
Replacing $\{0\}$ by the whole ideal of infinitesimals yields a weaker notion of \emph{archimedean element} that we call \emph{quasiarchimedean}. It is known that semisimple MV-algebras with compact maximal spectrum (in the co-Zarisky…
We show analogues of the classical Krein-Milman theorem for several ordered algebraic structures, especially in a semilattice (non-linear) framework. In that case, subsemilattices are seen as convex subsets, and for our proofs we use…
Complete MV-algebras are naturally equipped with frame structures. We call them MV-frames and investigate some of their main the properties as frames. We completely characterized algebraic MV-frames as well as regular MV-frames. In…
For any $n$-ary associative algebra we construct a $\Z_{n-1}$ graded algebra, which is a universal object containing the $n$-ary algebra as a subspace of elements of degree 1. Similar construction is carried out for semigroups.
In this paper, we show Kazhdan-Lusztig categories, that is, the categories of lower bounded generalized weight modules for certain affine vertex operator superalgebras that are locally finite modules of the underlying finite dimensional Lie…
This paper concerns the notion of a symmetric algebra and its generalization to a quasi-symmetric algebra. We study the structure of these algebras in respect to their hull-kernel regularity and existence of some ideals, especially the…
This paper aims at connecting the various classes that provide an algebraic semantics for three different conservative expansions of Lukasiewicz logic, using algebraic and category-theoretical techniques. We connect such classes of algebras…
In this paper, we introduce the concept of a (lattice) skew Hilbert algebra as a natural generalization of Hilbert algebras. This notion allows a unified treatment of several structures of prominent importance for mathematical logic, e.g.…
We investigate some new classes of operator algebras which we call semi-$\sigma$-finite subdiagonal and Riesz approximable. These constitute the most general setting to date for a noncommutative Hardy space theory based on Arveson's…
We describe the structure and different features of Lie algebras in the Verlinde category, obtained as semisimplification of contragredient Lie algebras in characteristic $p$ with respect to the adjoint action of a Chevalley generator. In…
We introduce a two-sorted algebraic theory whose models are states of MV-algebras and, to within a categorical equivalence that extends Mundici's well-known one, states of Abelian lattice-groups with (strong order) unit. We discuss free…
Let $G$ be a non-compact classical semisimple Lie group and let $G/V$ be the adjoint orbit with respect to a fixed element in $G$. These manifolds can be equipped with an almost-K\"ahler structure and we provide explicit formulae for the…
We classify the Rauzy-Veech groups of all connected components of all strata of the moduli space of translation surfaces in absolute homology, showing, in particular, that they are commensurable to arithmetic lattices of symplectic groups.…
A mixed lattice is a lattice-type structure consisting of a set with two partial orderings, and generalizing the notion of a lattice. Mixed lattice theory has previously been studied in various algebraic structures, such as groups and…
We establish a surprisingly close relationship between universal Horn classes of directed graphs and varieties generated by so-called adjacency semigroups which are Rees matrix semigroups over the trivial group with the unary operation of…
We describe representation theorems for local and perfect MV-algebras in terms of ultraproducts involving the unit interval [0,1]. Furthermore, we give a representation of local Abelian lattice-ordered groups with strong unit as…
We establish, generalizing Di Nola and Lettieri's categorical equivalence, a Morita-equivalence between the theory of lattice-ordered abelian groups and that of perfect MV-algebras. Further, after observing that the two theories are not…