Pseudo-BL algebras and pseudo-effect algebras arose in two rather different fields: fuzzy logics and quantum logics. In this paper, by introducing the notion of pseudo-weak MV-effect algebra which is non-commutative generalization of weak MV-effect algebra, we investigate the mutual relationship between pseudo-BL algebras and pseudo-effect algebras. We prove that dual pseudo-BL algebra under ce...

The Cartan decomposition in a semisimple Lie group is a generalization of the polar decomposition of matrices. In this paper we consider an even more general setting in which one obtains an analogous decomposition. In the semisimple case, this decomposition was worked out in a seminal paper of G. I. Ol'shanski 13]. In this paper we give general necessary and suucient conditions for this decompo...

In this paper, we mainly discuss linear deformations of a Hom-Lie-Yamaguti algebra and introduce the notion Hom-Nijenhuis operator. We product structure on algebra, which is operator E satisfying E2 = Id. There an involutive if only direct sum two subalgebras (as vector spaces). At same time, also complex algebra. Finally, add compatibility condition between to

Algorithmic issues concerning Elliott local semigroups are seldom considered in the literature, although these combinatorial structures completely classify AF algebras. In general, the addition operation of an Elliott local semigroup is partial, but for every AF algebra B whose Murray-von Neumann order of projections is a lattice, this operation is uniquely extendible to the addition of an invo...

An involutive Stone algebra (IS-algebra) is simultaneously a De Morgan and (i.e., pseudo-complemented distributive lattice satisfying the identity $$\mathop {\sim }x \vee \mathop }\mathop \approx 1$$ ). IS-algebras have been studied algebraically topologically since 1980s, but corresponding logic (here denoted $$\mathcal {IS}_{\le }$$ ) has introduced only very recently. This departing point of...

In Palmigiano and Re (J Pure Appl Algebra 215(8):1945–1957, 2011), spatial SGF-quantales are axiomatically introduced and proved to be representable as sub unital involutive quantales of quantales arising from set groupoids. In the present paper, spatial SGF-quantales of this class are shown to be optimally representable as unital involutive quantales of relations. The results of the present pa...

Among P−pseudo-Hermitian Hamiltonians H = P HP with real spectra, the “weakly pseudo-Hermitian” ones (i.e., those employing non-self-adjoint P 6 = P) form a remarkable subfamily. We list some reasons why it deserves a special attention. In particular we show that whenever P 6 = P, the current involutive operator of charge C gets complemented by a nonequivalent alternative involutive quasiparity...

We define and investigate a geometric object, called an associative geometry, corresponding to an associative algebra (and, more generally, to an associative pair). Associative geometries combine aspects of Lie groups and of generalized projective geometries, where the former correspond to the Lie product of an associative algebra and the latter to its Jordan product. A further development of t...

In 1982 Richard P. Stanley conjectured that any finitely generated Zn-graded module M over a finitely generated Nn-graded K-algebra R can be decomposed in a direct sum M = ⊕t i=1 νi Si of finitely many free modules νi Si which have to satisfy some additional conditions. Besides homogeneity conditions the most important restriction is that the Si have to be subalgebras of R of dimension at least...