For each 1 < s < ∞, a Popa algebra As is constructed that embeds as a weakly dense C∗–subalgebra of the interpolated free group factor L(Fs). Certain approximation properties for As are shown. It follows that L(Fs) has the weak expectation property of Lance with respect to As. In the course of the demonstration, it is proved that under certain conditions, full amalgamated free products of matri...

The purpose of this document is to develop some the basic theory multipliers algebra dual BCK-algebras. In study we demonstrate concept left bi-multiplier and right BCK (DBCK-algebra) algebras. Several examples results pertaining these on DBCK-algebras are developed based definitions. Then characteristics bi-multipliers obtained properties DBCK-algebras. We focused behavior elements under also ...

A class of non-semisimple matrix loop algebras consisting of triangular block matrices is introduced and used to generate bi-integrable couplings of soliton equations from zero curvature equations. The variational identities under non-degenerate, symmetric and ad-invariant bilinear forms are used to furnish Hamiltonian structures of the resulting bi-integrable couplings. A special case of the s...

This paper aims is to introduce states, Bosbach states and state-morphism operators on BI-algebras. We define state ideals BI-algebras give a characterization of the least ideal BI-algebra. It proved that kernel BI-algebra X an X. Further, by these concepts, we notions The notion complement pairs defined, proves under suitable conditions, there one-to-one correspondence between

We prove that discrete compact quantum groups (or more generally locally compact, under additional hypotheses) with coamenable dual are continuous fields over their central closed subgroups, and the same holds for free products of amalgamated a common subgroup. Along way we also show [Formula: see text]-algebras again via Fell-topology characterization text]-field continuity, recovering result ...