Regular Lie groups are infinite dimensional Lie groups with the property that smooth curves in the Lie algebra integrate to smooth curves in the group in a smooth way (an ‘evolution operator’ exists). Up to now all known smooth Lie groups are regular. We show in this paper that regular Lie groups allow to push surprisingly far the geometry of principal bundles: parallel transport exists and fla...

A C-metric algebra consists of a unital C-algebra and a Leibniz Lip-norm on the C-algebra. We show that if the Lip-norms concerned are lower semicontinuous, then any unital -homomorphism from a C-metric algebra to another one is necessarily Lipschitz. It results that the free product of two Lipschitz unital -homomorphisms between C-metric algebras coming from -filtrations is still a Lipschitz u...

We introduce a notion of “hopfish algebra” structure on an associative algebra, allowing the structure morphisms (coproduct, counit, antipode) to be bimodules rather than algebra homomorphisms. We prove that quasi-Hopf algebras are examples of hopfish algebras. We find that a hopfish structure on the algebra of functions on a finite set G is closely related to a “hypergroupoid” structure on G. ...

We study the minor relation for algebra homomorphims in finitely generated quasivarieties that admit a logarithmic natural duality. characterize homomorphism posets of finite algebras terms disjoint unions dual partition lattices and investigate reconstruction problems homomorphisms.

With the deep study in this work, we introduce concept of filters a bitonic algebra A. We some fundamental structures such determined filters. also focus on features with respect to homomorphisms. help idea upper sets, investigate basic ideas algebra, and state important theorems related them. obtain relations between algebras sets. an equivalent condition notion