In this paper, we introduce an algebra H from a subspace lattice with respect to a fixed flag which contains its incidence algebra as a proper subalgebra. We then establish a relation between the algebra H and the quantum affine algebra Uq1/2(ŝl2), where q denotes the cardinality of the base field. It is an extension of the well-known relation between the incidence algebra of a subspace lattice...

Let be a distance-regular graph of diameter D. Let X denote the vertex set of and let Y be a nonempty subset of X . We define an algebra T = T (Y ). This algebra is finite dimensional and semisimple. If Y consists of a single vertex then T is the corresponding subconstituent algebra defined by P. Terwilliger. We investigate the irreducible T -modules. We define endpoints and thin condition on i...

The main purpose of this paper is to axiomatize the join of the variety DPCSHC of dually pseudocomplemented semi-Heyting algebras generated by chains and the variety generated by D2, the De Morgan expansion of the four element Boolean Heyting algebra. Toward this end, we first introduce the variety DQDLNSH of dually quasi-De Morgan linear semi-Heyting algebras defined by the linearity axiom and...

Flaminio and Montagna (2008) enlarged the language of MV-algebras by a unary operation σ, called internal state or a state operator, equationally defined so as to preserve the basic properties of a state in its usual meaning. The resulting class of MV-algebras is called state MV-algebras. Jenča (2007) and Vetterlein (2008), using different approaches, represented MV-algebras through the quotien...

The main aim of this paper is to give classes of irreducible infinite dimensional representations and of irreducible *-representations of the q-deformed algebra U ′ q (so 2,2) which is a real form of the non-standard deformation U ′ q (so 4) of the universal enveloping algebra U (so(4, C)). These representations are described by two complex parameters and are obtained by " analytical continuati...

We consider the families L of propositional superintuitionistic logics (s.i.l.) andNE(K) of normal modal logics (n.m.l.). It is well known that there is a duality between L and the lattice of varieties of pseudo-boolean algebras (or Heyting algebras), and also NE(K) is dually isomorphic to the lattice of varieties of modal algebras. Many important properties of logics, for instance, Craig’s int...

The variety of Heyting algebras has two well-behaved locally finite reducts, the variety of bounded distributive lattices and the variety of implicative semilattices. The variety of bounded distributive lattices is generated by the→-free reducts of Heyting algebras while the variety of implicative semilattices by the ∨-free reducts. Each of these reducts gives rise to canonical formulas that ge...

It is shown that a separable C*-algebra is inner quasidiagonal if and only if it has a separating family of quasidiagonal irreducible representations. As a consequence, a separable C*-algebra is a strong NF algebra if and only if it is nuclear and has a separating family of quasidiagonal irreducible representations. We also obtain some permanence properties of the class of inner quasidiagonal C...

The natural join and the inner union operations combine relations in a database. Tropashko and Spight realized that these two operations are the meet and join operations in a class of lattices, known by now as the relational lattices. They proposed then lattice theory as an algebraic approach, alternative to the relational algebra, to the theory of databases. Litak et al. proposed an axiomatiza...

We show that the support of an irreducible weight module over the W -algebra W (2, 2), which has an infinite dimensional weight space, coincides with the weight lattice and that all nontrivial weight spaces of such a module are infinite dimensional. As a corollary, we obtain that every irreducible weight module over the the W -algebra W (2, 2), having a nontrivial finite dimensional weight spac...