Let V be any vector bundle over the sphere S n which is associated to the principal bundle of oriented orthonormal frames, or to that of spin frames. We give an explicit formula for the spectrum, with multiplicity, of the Bochner Laplacian r r on V , where r is the Riemannian or Riemannian spin connection. In the case of tensor bundles, we also give the spectrum of the Lichnerowicz Laplacian. T...

In [7] we introduced the category MKHaus of modal compact Hausdorff spaces, and showed these were concrete realizations of coalgebras for the Vietoris functor on compact Hausdorff spaces, much as modal spaces are coalgebras for the Vietoris functor on Stone spaces. Also in [7] we introduced the categories MKRFrm and MDV of modal compact regular frames, and modal de Vries algebras as algebraic c...

Quantum algebraic observables representing localization in space-time of a Dirac electron are defined. Inertial motion of the electron is represented in the quantum algebra with electron mass acting as the generator of motion. Since transformations to uniformly accelerated frames are naturally included in this conformally invariant description, the quantum algebra is also able to deal with unif...

The invariants of solvable Lie algebras with nilradicals isomorphic to the algebra of strongly upper triangular matrices and diagonal nilindependent elements are studied exhaustively. Bases of the invariant sets of all such algebras are constructed by an original purely algebraic algorithm based on Cartan’s method of moving frames.

This paper is an attempt to develop quantitative domain theory over frames. Firstly, we propose the notion of a fuzzy basis, and several equivalent characterizations of fuzzy bases are obtained. Furthermore, the concept of a fuzzy algebraic domain is introduced, and a relationship between fuzzy algebraic domains and fuzzy domains is discussed from the viewpoint of fuzzy basis. We finally give a...

in this paper, let $l$ be a completeresiduated lattice, and let {bf set} denote the category of setsand mappings, $lf$-{bf pos} denote the category of $lf$-posets and$lf$-monotone mappings, and $lf$-{bf cslat}$(sqcup)$, $lf$-{bfcslat}$(sqcap)$ denote the category of $lf$-completelattices and $lf$-join-preserving mappings and the category of$lf$-complete lattices and $lf$-meet-preserving mapping...

This talk is a contribution towards the project of developing discrete representability for the algebraic semantics of various non-classical logics. Discrete duality is a type of duality where a class of abstract relational systems is a dual counterpart to a class of algebras. These relational systems are referred to as ‘frames’ following the terminology of non-classical logics. There is no top...

Relational semantics, given by Kripke frames, play an essential role in the study of modal and intuitionistic logic. In [DGP05] it is shown that the theory of relational semantics is also available in the more general setting of substructural logic, at least in an algebraic guise. Building on these ideas, in [Geh06] a type of frames is described which generalise Kripke frames and provide semant...

The main objective of this paper is to show that the notion of type which was developed within the frames of logic and model theory has deep ties with geometric properties of algebras. These ties go back and forth from universal algebraic geometry to the model theory through the machinery of algebraic logic. We show that types appear naturally as logical kernels in the Galois correspondence bet...

• Introduction to the local differential geometry of submanifolds of projective space • Introduction to moving frames for projective geometry • How much must a submanifold X ⊂ PN resemble a given submanifold Z ⊂ PM infinitesimally before we can conclude X ≃ Z? • To what order must a line field on a submanifold X ⊂ PN have contact with X before we can conclude the lines are contained in X? • App...