Pseudoalgebras and Non-canonical Isomorphisms

A Note on Isomorphisms Between Canonical Frames

This paper looks at the question of what kinds of automorphisms and isomorphisms can exist within and between canonical frames for modal logics. Specifically, this paper is able to partially answer the question posed by the author in [7] of whether FL ! = FL !1 in the presence of the extra-ZFC axiom “2! = 2!1 .” We answer the question in the negative for all logics below S5 and for all logics s...

Theory of Finite Pseudoalgebras

Simple Finite Jordan Pseudoalgebras⋆

We consider the structure of JordanH-pseudoalgebras which are linearly finitely generated over a Hopf algebra H . There are two cases under consideration: H = U(h) and H = U(h)#C[Γ], where h is a finite-dimensional Lie algebra over C, Γ is an arbitrary group acting on U(h) by automorphisms. We construct an analogue of the Tits–Kantor–Koecher construction for finite Jordan pseudoalgebras and des...

Canonical and Non-canonical Reelin Signaling

Reelin is a large secreted glycoprotein that is essential for correct neuronal positioning during neurodevelopment and is important for synaptic plasticity in the mature brain. Moreover, Reelin is expressed in many extraneuronal tissues; yet the roles of peripheral Reelin are largely unknown. In the brain, many of Reelin's functions are mediated by a molecular signaling cascade that involves tw...

Lie Algebroids and Lie Pseudoalgebras

Lie algebroids and Lie pseudoalgebras arise from a wide variety of constructions in differential geometry; they have been introduced repeatedly into the geometry, physics and algebra literatures since the 1950s, under some 14 different terminologies. The first main part (Sections 2-5) of this survey describes the four principal classes of examples, emphazising that each arises by means of a gen...