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Injective Hulls are Completions of Ordered Algebras
It is well-known that the Dedekind-MacNeille completion of a poset is its injective hull. We prove that the injective hull of an ordered universal...
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Relative poset polytopes and semitoric degenerations
The two best studied toric degenerations of the flag variety are those given by the Gelfand–Tsetlin and FFLV polytopes. Each of them degenerates...
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Birational Maps to Grassmannians, Representations and Poset Polytopes
We study the closure of the graph of the birational map from a projective space to a Grassmannian. We provide explicit description of the graph...
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Notes on Sharp and Principal Elements in Effect Algebras
In this paper, we characterize the sharp elements and principal elements in effect algebras. Furthermore, the sufficient and necessary conditions for E
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Triangulations of flow polytopes, ample framings, and gentle algebras
The cone of nonnegative flows for a directed acyclic graph (DAG) is known to admit regular unimodular triangulations induced by framings of the DAG....
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Esakia duals of regular Heyting algebras
We investigate in this article regular Heyting algebras by means of Esakia duality. In particular, we give a characterisation of Esakia spaces dual...
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Homotopy prefactorization algebras
We apply the theory of operadic Koszul duality to provide a cofibrant resolution of the colored operad whose algebras are prefactorization algebras...
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Chain algebras of finite distributive lattices
We introduce a family of toric algebras defined by maximal chains of a finite distributive lattice. Applying results on stable set polytopes, we...
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Varieties of ordered algebras as categories
A variety is a category of ordered (finitary) algebras presented by inequations between terms. We characterize categories enriched over the category...
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Commutativity Preservers of Incidence Algebras
Let I ( X , K ) be the incidence algebra of a finite connected poset X over a field K and D ( X , K ) its subalgebra consisting of diagonal elements. We...
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Tilting Modules and Exceptional Sequences for a Family of Dual Extension Algebras
We provide a classification of generalized tilting modules and full exceptional sequences for a certain family of quasi-hereditary algebras, namely...
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Characterizations of near-Heyting algebras
A near-Heyting algebra is a join-semilattice with a greatest element such that every principal upset is a Heyting algebra. We will present several...
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Regular Hom-Lie structures on incidence algebras
We fully characterize regular Hom-Lie structures on the incidence algebra I ( X , K ) of a finite connected poset X over a field K . We prove that such a...
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On Local (like) Derivations on Path Algebras
In this paper, we investigate local derivations and local generalized derivations on path algebras associated with finite acyclic quivers. We show...
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Preservation of Order and Orthogonality on Preduals of Jordan Algebras
We study linear maps between preduals of JBW-algebras that preserve orthogonal decompositions of functionals. We generalize and strengthen results of...